i05nagai/mafipy

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mafipy/function/black_scholes.py

Summary

Maintainability
F
4 days
Test Coverage

File black_scholes.py has 643 lines of code (exceeds 250 allowed). Consider refactoring.
Open

from __future__ import division, print_function, absolute_import
import math
import numpy as np
import scipy.special

Severity: Major
Found in mafipy/function/black_scholes.py - About 1 day to fix

    Cyclomatic complexity is too high in function black_scholes_call_value. (14)
    Open

    def black_scholes_call_value(
            underlying,
            strike,
            rate,
            maturity,
    Severity: Minor
    Found in mafipy/function/black_scholes.py by radon

    Cyclomatic Complexity

    Cyclomatic Complexity corresponds to the number of decisions a block of code contains plus 1. This number (also called McCabe number) is equal to the number of linearly independent paths through the code. This number can be used as a guide when testing conditional logic in blocks.

    Radon analyzes the AST tree of a Python program to compute Cyclomatic Complexity. Statements have the following effects on Cyclomatic Complexity:

    Construct Effect on CC Reasoning
    if +1 An if statement is a single decision.
    elif +1 The elif statement adds another decision.
    else +0 The else statement does not cause a new decision. The decision is at the if.
    for +1 There is a decision at the start of the loop.
    while +1 There is a decision at the while statement.
    except +1 Each except branch adds a new conditional path of execution.
    finally +0 The finally block is unconditionally executed.
    with +1 The with statement roughly corresponds to a try/except block (see PEP 343 for details).
    assert +1 The assert statement internally roughly equals a conditional statement.
    Comprehension +1 A list/set/dict comprehension of generator expression is equivalent to a for loop.
    Boolean Operator +1 Every boolean operator (and, or) adds a decision point.

    Source: http://radon.readthedocs.org/en/latest/intro.html

    Cyclomatic complexity is too high in function black_scholes_call_value_fhess_by_strike. (9)
    Open

    def black_scholes_call_value_fhess_by_strike(
            underlying, strike, rate, maturity, vol):
        """black_scholes_call_value_fhess_by_strike
        Second derivative of value of call option with respect to strike
        under black scholes model.
    Severity: Minor
    Found in mafipy/function/black_scholes.py by radon

    Cyclomatic Complexity

    Cyclomatic Complexity corresponds to the number of decisions a block of code contains plus 1. This number (also called McCabe number) is equal to the number of linearly independent paths through the code. This number can be used as a guide when testing conditional logic in blocks.

    Radon analyzes the AST tree of a Python program to compute Cyclomatic Complexity. Statements have the following effects on Cyclomatic Complexity:

    Construct Effect on CC Reasoning
    if +1 An if statement is a single decision.
    elif +1 The elif statement adds another decision.
    else +0 The else statement does not cause a new decision. The decision is at the if.
    for +1 There is a decision at the start of the loop.
    while +1 There is a decision at the while statement.
    except +1 Each except branch adds a new conditional path of execution.
    finally +0 The finally block is unconditionally executed.
    with +1 The with statement roughly corresponds to a try/except block (see PEP 343 for details).
    assert +1 The assert statement internally roughly equals a conditional statement.
    Comprehension +1 A list/set/dict comprehension of generator expression is equivalent to a for loop.
    Boolean Operator +1 Every boolean operator (and, or) adds a decision point.

    Source: http://radon.readthedocs.org/en/latest/intro.html

    Cyclomatic complexity is too high in function black_scholes_put_value. (7)
    Open

    def black_scholes_put_value(
            underlying,
            strike,
            rate,
            maturity,
    Severity: Minor
    Found in mafipy/function/black_scholes.py by radon

    Cyclomatic Complexity

    Cyclomatic Complexity corresponds to the number of decisions a block of code contains plus 1. This number (also called McCabe number) is equal to the number of linearly independent paths through the code. This number can be used as a guide when testing conditional logic in blocks.

    Radon analyzes the AST tree of a Python program to compute Cyclomatic Complexity. Statements have the following effects on Cyclomatic Complexity:

    Construct Effect on CC Reasoning
    if +1 An if statement is a single decision.
    elif +1 The elif statement adds another decision.
    else +0 The else statement does not cause a new decision. The decision is at the if.
    for +1 There is a decision at the start of the loop.
    while +1 There is a decision at the while statement.
    except +1 Each except branch adds a new conditional path of execution.
    finally +0 The finally block is unconditionally executed.
    with +1 The with statement roughly corresponds to a try/except block (see PEP 343 for details).
    assert +1 The assert statement internally roughly equals a conditional statement.
    Comprehension +1 A list/set/dict comprehension of generator expression is equivalent to a for loop.
    Boolean Operator +1 Every boolean operator (and, or) adds a decision point.

    Source: http://radon.readthedocs.org/en/latest/intro.html

    Function black_scholes_call_value has a Cognitive Complexity of 9 (exceeds 5 allowed). Consider refactoring.
    Open

    def black_scholes_call_value(
            underlying,
            strike,
            rate,
            maturity,
    Severity: Minor
    Found in mafipy/function/black_scholes.py - About 55 mins to fix

    Cognitive Complexity

    Cognitive Complexity is a measure of how difficult a unit of code is to intuitively understand. Unlike Cyclomatic Complexity, which determines how difficult your code will be to test, Cognitive Complexity tells you how difficult your code will be to read and comprehend.

    A method's cognitive complexity is based on a few simple rules:

    • Code is not considered more complex when it uses shorthand that the language provides for collapsing multiple statements into one
    • Code is considered more complex for each "break in the linear flow of the code"
    • Code is considered more complex when "flow breaking structures are nested"

    Further reading

    Function black_scholes_call_value has 6 arguments (exceeds 4 allowed). Consider refactoring.
    Open

    def black_scholes_call_value(
    Severity: Minor
    Found in mafipy/function/black_scholes.py - About 45 mins to fix

      Function black_scholes_call_theta has 6 arguments (exceeds 4 allowed). Consider refactoring.
      Open

      def black_scholes_call_theta(underlying, strike, rate, maturity, vol, today):
      Severity: Minor
      Found in mafipy/function/black_scholes.py - About 45 mins to fix

        Function black_scholes_put_value has 6 arguments (exceeds 4 allowed). Consider refactoring.
        Open

        def black_scholes_put_value(
        Severity: Minor
        Found in mafipy/function/black_scholes.py - About 45 mins to fix

          Function black_scholes_call_rho has 6 arguments (exceeds 4 allowed). Consider refactoring.
          Open

          def black_scholes_call_rho(underlying, strike, rate, maturity, vol, today):
          Severity: Minor
          Found in mafipy/function/black_scholes.py - About 45 mins to fix

            Consider simplifying this complex logical expression.
            Open

                if time < 0.0 or np.isclose(time, 0.0):
                    return 0.0
                elif np.isclose(underlying, 0.0):
                    return math.exp(-rate * time) * max(-strike, 0.0)
                elif np.isclose(strike, 0.0) and underlying > 0.0:
            Severity: Major
            Found in mafipy/function/black_scholes.py - About 40 mins to fix

              Function black_scholes_call_delta has 5 arguments (exceeds 4 allowed). Consider refactoring.
              Open

              def black_scholes_call_delta(underlying, strike, rate, maturity, vol):
              Severity: Minor
              Found in mafipy/function/black_scholes.py - About 35 mins to fix

                Function black_scholes_cdf has 5 arguments (exceeds 4 allowed). Consider refactoring.
                Open

                def black_scholes_cdf(underlying, strike, rate, maturity, vol):
                Severity: Minor
                Found in mafipy/function/black_scholes.py - About 35 mins to fix

                  Function black_scholes_call_volga has 5 arguments (exceeds 4 allowed). Consider refactoring.
                  Open

                  def black_scholes_call_volga(underlying, strike, rate, maturity, vol):
                  Severity: Minor
                  Found in mafipy/function/black_scholes.py - About 35 mins to fix

                    Function d_fprime_by_strike has 5 arguments (exceeds 4 allowed). Consider refactoring.
                    Open

                    def d_fprime_by_strike(underlying, strike, rate, maturity, vol):
                    Severity: Minor
                    Found in mafipy/function/black_scholes.py - About 35 mins to fix

                      Function black_scholes_put_formula has 5 arguments (exceeds 4 allowed). Consider refactoring.
                      Open

                      def black_scholes_put_formula(underlying, strike, rate, maturity, vol):
                      Severity: Minor
                      Found in mafipy/function/black_scholes.py - About 35 mins to fix

                        Function func_d1 has 5 arguments (exceeds 4 allowed). Consider refactoring.
                        Open

                        def func_d1(underlying, strike, rate, maturity, vol):
                        Severity: Minor
                        Found in mafipy/function/black_scholes.py - About 35 mins to fix

                          Function func_d2 has 5 arguments (exceeds 4 allowed). Consider refactoring.
                          Open

                          def func_d2(underlying, strike, rate, maturity, vol):
                          Severity: Minor
                          Found in mafipy/function/black_scholes.py - About 35 mins to fix

                            Function black_scholes_call_formula has 5 arguments (exceeds 4 allowed). Consider refactoring.
                            Open

                            def black_scholes_call_formula(underlying, strike, rate, maturity, vol):
                            Severity: Minor
                            Found in mafipy/function/black_scholes.py - About 35 mins to fix

                              Function black_scholes_pdf has 5 arguments (exceeds 4 allowed). Consider refactoring.
                              Open

                              def black_scholes_pdf(underlying, strike, rate, maturity, vol):
                              Severity: Minor
                              Found in mafipy/function/black_scholes.py - About 35 mins to fix

                                Function black_scholes_call_value_fprime_by_strike has 5 arguments (exceeds 4 allowed). Consider refactoring.
                                Open

                                def black_scholes_call_value_fprime_by_strike(
                                Severity: Minor
                                Found in mafipy/function/black_scholes.py - About 35 mins to fix

                                  Function black_scholes_call_value_fhess_by_strike has 5 arguments (exceeds 4 allowed). Consider refactoring.
                                  Open

                                  def black_scholes_call_value_fhess_by_strike(
                                  Severity: Minor
                                  Found in mafipy/function/black_scholes.py - About 35 mins to fix

                                    Function black_scholes_call_value_third_by_strike has 5 arguments (exceeds 4 allowed). Consider refactoring.
                                    Open

                                    def black_scholes_call_value_third_by_strike(
                                    Severity: Minor
                                    Found in mafipy/function/black_scholes.py - About 35 mins to fix

                                      Function d_fhess_by_strike has 5 arguments (exceeds 4 allowed). Consider refactoring.
                                      Open

                                      def d_fhess_by_strike(underlying, strike, rate, maturity, vol):
                                      Severity: Minor
                                      Found in mafipy/function/black_scholes.py - About 35 mins to fix

                                        Function black_scholes_call_gamma has 5 arguments (exceeds 4 allowed). Consider refactoring.
                                        Open

                                        def black_scholes_call_gamma(underlying, strike, rate, maturity, vol):
                                        Severity: Minor
                                        Found in mafipy/function/black_scholes.py - About 35 mins to fix

                                          Function black_scholes_call_vega_fprime_by_strike has 5 arguments (exceeds 4 allowed). Consider refactoring.
                                          Open

                                          def black_scholes_call_vega_fprime_by_strike(
                                          Severity: Minor
                                          Found in mafipy/function/black_scholes.py - About 35 mins to fix

                                            Function black_scholes_call_vega has 5 arguments (exceeds 4 allowed). Consider refactoring.
                                            Open

                                            def black_scholes_call_vega(underlying, strike, rate, maturity, vol):
                                            Severity: Minor
                                            Found in mafipy/function/black_scholes.py - About 35 mins to fix

                                              Avoid too many return statements within this function.
                                              Open

                                                      return 0.0
                                              Severity: Major
                                              Found in mafipy/function/black_scholes.py - About 30 mins to fix

                                                Avoid too many return statements within this function.
                                                Open

                                                        return underlying - math.exp(-rate * time) * strike
                                                Severity: Major
                                                Found in mafipy/function/black_scholes.py - About 30 mins to fix

                                                  Avoid too many return statements within this function.
                                                  Open

                                                      return black_scholes_call_formula(
                                                  Severity: Major
                                                  Found in mafipy/function/black_scholes.py - About 30 mins to fix

                                                    Avoid too many return statements within this function.
                                                    Open

                                                            return (underlying - strike) + value
                                                    Severity: Major
                                                    Found in mafipy/function/black_scholes.py - About 30 mins to fix

                                                      Function black_scholes_call_value_fhess_by_strike has a Cognitive Complexity of 6 (exceeds 5 allowed). Consider refactoring.
                                                      Open

                                                      def black_scholes_call_value_fhess_by_strike(
                                                              underlying, strike, rate, maturity, vol):
                                                          """black_scholes_call_value_fhess_by_strike
                                                          Second derivative of value of call option with respect to strike
                                                          under black scholes model.
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py - About 25 mins to fix

                                                      Cognitive Complexity

                                                      Cognitive Complexity is a measure of how difficult a unit of code is to intuitively understand. Unlike Cyclomatic Complexity, which determines how difficult your code will be to test, Cognitive Complexity tells you how difficult your code will be to read and comprehend.

                                                      A method's cognitive complexity is based on a few simple rules:

                                                      • Code is not considered more complex when it uses shorthand that the language provides for collapsing multiple statements into one
                                                      • Code is considered more complex for each "break in the linear flow of the code"
                                                      • Code is considered more complex when "flow breaking structures are nested"

                                                      Further reading

                                                      Similar blocks of code found in 2 locations. Consider refactoring.
                                                      Open

                                                          numerator = (
                                                              math.log(underlying / strike) + (rate - vol * vol * 0.5) * maturity)
                                                      Severity: Major
                                                      Found in mafipy/function/black_scholes.py and 1 other location - About 1 hr to fix
                                                      mafipy/function/tests/test_black_scholes.py on lines 82..83

                                                      Duplicated Code

                                                      Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                                                      Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                                                      When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                                                      Tuning

                                                      This issue has a mass of 47.

                                                      We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                                                      The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                                                      If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                                                      See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                                                      Refactorings

                                                      Further Reading

                                                      Similar blocks of code found in 2 locations. Consider refactoring.
                                                      Open

                                                          numerator = (
                                                              math.log(underlying / strike) + (rate + vol * vol * 0.5) * maturity)
                                                      Severity: Major
                                                      Found in mafipy/function/black_scholes.py and 1 other location - About 1 hr to fix
                                                      mafipy/function/tests/test_black_scholes.py on lines 65..66

                                                      Duplicated Code

                                                      Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                                                      Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                                                      When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                                                      Tuning

                                                      This issue has a mass of 47.

                                                      We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                                                      The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                                                      If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                                                      See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                                                      Refactorings

                                                      Further Reading

                                                      Similar blocks of code found in 2 locations. Consider refactoring.
                                                      Open

                                                          term2 = rate * math.exp(-rate * time) * strike * norm.cdf(d2)
                                                      Severity: Major
                                                      Found in mafipy/function/black_scholes.py and 1 other location - About 1 hr to fix
                                                      mafipy/function/black_scholes.py on lines 703..703

                                                      Duplicated Code

                                                      Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                                                      Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                                                      When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                                                      Tuning

                                                      This issue has a mass of 41.

                                                      We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                                                      The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                                                      If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                                                      See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                                                      Refactorings

                                                      Further Reading

                                                      Similar blocks of code found in 2 locations. Consider refactoring.
                                                      Open

                                                          return time * math.exp(-rate * time) * strike * norm.cdf(d2)
                                                      Severity: Major
                                                      Found in mafipy/function/black_scholes.py and 1 other location - About 1 hr to fix
                                                      mafipy/function/black_scholes.py on lines 664..664

                                                      Duplicated Code

                                                      Duplicated code can lead to software that is hard to understand and difficult to change. The Don't Repeat Yourself (DRY) principle states:

                                                      Every piece of knowledge must have a single, unambiguous, authoritative representation within a system.

                                                      When you violate DRY, bugs and maintenance problems are sure to follow. Duplicated code has a tendency to both continue to replicate and also to diverge (leaving bugs as two similar implementations differ in subtle ways).

                                                      Tuning

                                                      This issue has a mass of 41.

                                                      We set useful threshold defaults for the languages we support but you may want to adjust these settings based on your project guidelines.

                                                      The threshold configuration represents the minimum mass a code block must have to be analyzed for duplication. The lower the threshold, the more fine-grained the comparison.

                                                      If the engine is too easily reporting duplication, try raising the threshold. If you suspect that the engine isn't catching enough duplication, try lowering the threshold. The best setting tends to differ from language to language.

                                                      See codeclimate-duplication's documentation for more information about tuning the mass threshold in your .codeclimate.yml.

                                                      Refactorings

                                                      Further Reading

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is vol,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial^{2}}{\partial K^{2}} d_{1}(K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\l'
                                                      Open

                                                                  \\frac{\ln(S/K) + (r + \sigma^{2}/2)T}{\sigma \sqrt{T}},
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\c'
                                                      Open

                                                          :math:`N(\cdot)` is standard normal distribution,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial }{\partial K} d_{1}(K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial^{2}}{\partial K^{2}} d_{1}(K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              = \\frac{1}{S \sigma \sqrt{T} },
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              = \\frac{\partial }{\partial K} d_{2}(K).
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial }{\partial K} d_{1}(K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial }{\partial K} d_{1}(K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is vol,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              = \\frac{1}{S \sigma \sqrt{T} },
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              = \\frac{\partial }{\partial K} d_{2}(K).
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial }{\partial K} d_{1}(K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              =  \\frac{K}{\sigma S \sqrt{T}}.
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              =  \\frac{K}{\sigma S \sqrt{T}}.
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\ '
                                                      Open

                                                          second derivative of :math:`d_{i}\ (i = 1, 2)` with respect to :math:`K`,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                  \\frac{\ln(S/K) + (r + \sigma^{2}/2)T}{\sigma \sqrt{T}},
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                  \\frac{\ln(S/K) + (r - \sigma^{2}/2)T} {\sigma \sqrt{T}},
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                      & = & c(S, K, r, T, \sigma) - e^{-rT}(S - K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\c'
                                                      Open

                                                          :math:`\phi(\cdot)` is p.d.f. of standard normal distribution.
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                              + \phi(d_{2}(K))d^{\prime\prime}(K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                      \\frac{1}{S^{2}\sigma\sqrt{T}}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is volatility,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                  = \sqrt{T}S\phi(d_{1}(S, K, r, T, \sigma))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                  = \sqrt{T}S\phi(d_{1}(S, K, r, T, \sigma))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                  = \sqrt{T}S\phi(d_{1}(S, K, r, T, \sigma))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                  S \phi^{\prime}(d_{1}(\sigma))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial}{\partial t} c(t, S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\i'
                                                      Open

                                                                  \iff & p(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                  \iff & p(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\c'
                                                      Open

                                                          :math:`p(\cdot)` denotes value of put option,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial }{\partial K} c(K; S, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is vol,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                              + \phi(d_{2}(K))d^{\prime\prime}(K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is volatility,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              \\frac{\partial}{\partial t} c(t, S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                          \\frac{\sigma}{2\sqrt{T - t}}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                      K \Phi(d_{2})
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              S\phi^{\prime}(d_{1}(S, K, r, T, \sigma))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\l'
                                                      Open

                                                                      \left(
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is vol,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\phi(\cdot)` is p.d.f. of standard normal distribution.
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial^{2}}{\partial S^{2}} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\phi` is standard normal p.d.f,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial}{\partial K}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\Phi(\cdot)` is c.d.f. of standard normal distribution,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\Phi(\cdot)` is c.d.f. of standard normal distribution,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                      \\frac{1}{S^{2}\sigma\sqrt{T}}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial}{\partial t} c(t, S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\l'
                                                      Open

                                                                      \left(
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              S\phi^{\prime}(d_{1}(S, K, r, T, \sigma))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                  \\frac{\ln(S/K) + (r + \sigma^{2}/2)T}{\sigma \sqrt{T}},
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\e'
                                                      Open

                                                              \end{array}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              \\frac{\partial }{\partial K} c(K; S, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                  \\frac{\partial^{2}}{\partial K^{2}} c(0, S; T, K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                          \phi(d_{2}(K)) d^{\prime}(K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\phi(\cdot)` is p.d.f. of standard normal distribution.
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                              + \phi(d_{2}(K))d^{\prime\prime}(K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                  = - S * \phi(d_{1})
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is volatility,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                  \\frac{\ln(S/K) + (r - \sigma^{2}/2)T} {\sigma \sqrt{T}},
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                      & = & c(S, K, r, T, \sigma) - p(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\c'
                                                      Open

                                                          :math:`\Phi(\cdot)` is c.d.f. of standard normal distribution,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                      \sigma^{2}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is volatility,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\m'
                                                      Open

                                                              \mathrm{Vega}{\mathrm{BSCall}}(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\e'
                                                      Open

                                                              \end{eqnarray}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                  \\frac{\partial^{2}}{\partial K^{2}} c(0, S; T, K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                  \\frac{\partial^{3}}{\partial K^{3}} c(0, S; T, K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\Phi` is standard normal c.d.f,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial^{2}}{\partial \sigma^{2}} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\phi` is standard normal p.d.f,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial}{\partial t} c(t, S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\m'
                                                      Open

                                                              \mathrm{Vega}{\mathrm{BSCall}}(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              \mathrm{Vega}{\mathrm{BSCall}}(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              \\frac{1}{\sigma K}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\phi` is standard normal p.d.f,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial }{\partial K} c(K; S, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              = - e^{-rT} \Phi(d_{1}(K))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial}{\partial K}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                  \\frac{\ln(S/K) + (r + \sigma^{2}/2)T}{\sigma \sqrt{T}},
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                      & = & c(S, K, r, T, \sigma) - p(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                          \phi^{\prime}(d_{2}(K))(d^{\prime}(K))^{2}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                          \phi^{\prime}(d_{2}(K))(d^{\prime}(K))^{2}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                          \phi^{\prime}(d_{2}(K))(d^{\prime}(K))^{2}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial}{\partial \sigma} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              \\frac{\partial}{\partial \sigma} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is volatility,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\phi` is standard normal p.d.f,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is vol,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                  = \Phi(d_{1}(S))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is volatility,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial^{2}}{\partial \sigma^{2}} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                      (\\frac{1}{2} \sigma^{2} - r)T
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              \\frac{\partial}{\partial t} c(t, S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\l'
                                                      Open

                                                          * case :math:`T \le 0`
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                          \phi(d_{2}(K)) d^{\prime}(K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\Phi(\cdot)` is c.d.f. of standard normal distribution,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                  = -\phi(d_{1}(S, K, r, T, \sigma))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\phi` is standard normal p.d.f,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              S\phi^{\prime}(d_{1}(S, K, r, T, \sigma))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\c'
                                                      Open

                                                          :math:`\Phi(\cdot)` is c.d.f. of standard normal distribution,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\e'
                                                      Open

                                                              \end{array}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\c'
                                                      Open

                                                          :math:`\Phi(\cdot)` is c.d.f. of standard normal distribution,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\e'
                                                      Open

                                                              \end{array}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\c'
                                                      Open

                                                          :math:`c(\cdot)` denotes value of call option,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\c'
                                                      Open

                                                          :math:`\phi(\cdot)` is p.d.f. of standard normal distribution.
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial}{\partial S} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial}{\partial S} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                          \\frac{\sigma}{2\sqrt{T - t}}
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                      - r e^{-r(T - t)} K \Phi(d_{2})
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is volatility,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                  \\frac{\ln(S/K) + (r - \sigma^{2}/2)T} {\sigma \sqrt{T}},
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\c'
                                                      Open

                                                          :math:`c(\cdot)` is calculated
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\phi(\cdot)` is p.d.f. of standard normal distribution.
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\c'
                                                      Open

                                                          :math:`\phi(\cdot)` is p.d.f. of standard normal distribution.
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                  \\frac{\partial^{3}}{\partial K^{3}} c(0, S; T, K)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial^{2}}{\partial S^{2}} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              \\frac{\partial}{\partial \sigma} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                                  S \phi^{\prime}(d_{1}(\sigma))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                  S \phi^{\prime}(d_{1}(\sigma))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                          :math:`\sigma` is vol.
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              \\frac{\partial}{\partial S} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              \\frac{\partial^{2}}{\partial S^{2}} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              \\frac{\partial^{2}}{\partial \sigma^{2}} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\l'
                                                      Open

                                                                  \\frac{\ln(S/K) + (r - \sigma^{2}/2)T} {\sigma \sqrt{T}},
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                          :math:`\Phi` is standard normal c.d.f,
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                                  = -\phi(d_{1}(S, K, r, T, \sigma))
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial}{\partial \sigma} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\s'
                                                      Open

                                                              \\frac{\partial^{2}}{\partial \sigma^{2}} c(S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      Invalid escape sequence '\p'
                                                      Open

                                                              \\frac{\partial}{\partial t} c(t, S, K, r, T, \sigma)
                                                      Severity: Minor
                                                      Found in mafipy/function/black_scholes.py by pep8

                                                      Invalid escape sequences are deprecated in Python 3.6.

                                                      Okay: regex = r'\.png$'
                                                      W605: regex = '\.png$'

                                                      There are no issues that match your filters.

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