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IntermediateOptions, Derivatives & FinanceJavaScript

Run this module

cd "Monte Carlo Simulation - JavaScript"
node "monteCarlo.js"

View source on GitHub

Monte Carlo Simulation – JavaScript

Overview

A pure JavaScript Monte Carlo engine for portfolio simulation and European option pricing via geometric Brownian motion (GBM). Implements correlated multi-asset paths using Cholesky decomposition, antithetic variates for variance reduction, and VaR/CVaR estimation from the simulated return distribution. No external dependencies — runs directly in Node.js.

Concepts Covered

  • Box-Muller transform for standard-normal random variate generation
  • Single-asset GBM path simulation
  • Cholesky decomposition to impose user-defined asset correlations
  • Multi-asset correlated portfolio simulation with equity curve tracking
  • European call option pricing via risk-neutral GBM with antithetic variates
  • Value-at-Risk (VaR) and Conditional VaR (CVaR) from simulated return distributions

Files

  • monteCarlo.js: Self-contained module; exports simulatePath, simulatePortfolio, mcOptionPrice, varCvar, randNormal, cholesky

How to Run

node monteCarlo.js
The demo runs three scenarios and prints results: a single GBM price path, a 10,000-path three-asset portfolio with risk metrics, and a 50,000-sim European call priced against the Black-Scholes analytical value.

API

const { simulatePath, simulatePortfolio, mcOptionPrice, varCvar } = require('./monteCarlo');

simulatePath(S0, mu, sigma, T, steps)
// Returns number[] — a single GBM price path of length steps + 1

simulatePortfolio(S0, mu, sigma, corr, weights, T, steps, nSims)
// Returns { finalReturns: number[], samplePaths: number[][] }
// samplePaths contains equity curves for the first 5 simulations

mcOptionPrice(S, K, T, r, sigma, nSims?)
// Returns { price: number, stdErr: number }

varCvar(returns, confidence?)
// Returns { var: number, cvar: number }

Exported Functions

Function Description
simulatePath Single GBM path (log-normal dynamics)
simulatePortfolio Multi-asset correlated paths via Cholesky; tracks equity curves
mcOptionPrice Risk-neutral European call pricing with antithetic variates
varCvar VaR and CVaR from a sorted returns array
randNormal Box-Muller standard-normal sampler
cholesky Lower-triangular Cholesky factor of a correlation matrix

Practice Ideas

  • Price a European put and verify put-call parity against Options Pricing - JavaScript/
  • Extend simulatePortfolio to compute drawdown statistics across all paths
  • Add an Asian option pricer by averaging the price path instead of using only the terminal value

Next Steps

  • Compare MC option prices to the analytical Black-Scholes formula in Options Pricing - JavaScript/
  • See the Python Monte Carlo equivalent in Quantitative Methods - Stochastic Processes/
  • Apply VaR/CVaR in a full risk pipeline with Risk Metrics/ and Value at Risk/

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