SockTrader/SockTrader

import { std } from '../statistics';
import { norminv } from '../statistics/norminv';
import { prctile } from '../statistics/prctile';

/**
 * @method  monteCarloValueAtRisk
 * @summary Montecarlo Value-at-Risk
 * @description Montecarlo VaR for single asset. Based on geometric Brownian motion.
 *
 * @param  {number|array} x array of returns or standard deviation of returns
 * @param  {number} p confidence level in the range [0,1] (def: 0.95)
 * @param  {number} t holding period (def: 1)
 * @param  {number} fr free-risk rate (def: 0)
 * @param  {number} v asset/portfolio start value (def: 1)
 * @param  {number} iter number of iterations
 * @return {number}
 *
 * @example
 * var x = [0.003,0.026,0.015,-0.009,0.014,0.024,0.015,0.066,-0.014,0.039];
 *
 * // ex-ante simulated VaR at 95% confidence for t = 1, free risk zero, start capital one
 * monteCarloValueAtRisk(x,0.95,1,0,1,10000);
 * // 0.073219
 *
 * // historical simulated daily VaR at 99% for 100k GBP asset over 10 days
 * monteCarloValueAtRisk(std(x),0.99,10,0,100000);
 * // 25254.640005
 */
export function monteCarloValueAtRisk(
  x: number[],
  p = 0.95,
  t = 1,
  fr = 0,
  v = 1,
  iter = 10000
): number {
  const s = std(x);
  const mcvar = [];
  for (let i = 0; i < iter; i++) {
    mcvar[i] =
      Math.exp(fr - 0.5 * Math.pow(s, 2) + s * norminv(Math.random(), 0, 1)) -
      1;
  }
  return -Math.pow(t, 0.5) * prctile(mcvar, 1 - p) * v;
}