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IntermediateOptions, Derivatives & FinanceJavaScript

Run this module

cd "Options Pricing - JavaScript"
node "blackScholes.js"

View source on GitHub

Options Pricing – JavaScript

Overview

A pure JavaScript implementation of the Black-Scholes European options pricing model with all five Greeks and implied volatility via bisection. No external dependencies — runs directly in Node.js and can be imported as a module into any JS project.

Concepts Covered

  • Cumulative standard normal CDF (Abramowitz & Stegun approximation, error < 7.5e-8)
  • Black-Scholes price formula for European calls and puts
  • All five Greeks: delta, gamma, theta (daily decay), vega (per 1% vol move), rho (per 1% rate move)
  • Implied volatility extraction via bisection search
  • Put-call parity verification as a correctness check

Files

  • blackScholes.js: Self-contained module; exports price, greeks, impliedVol, normCdf, normPdf

How to Run

node blackScholes.js
The demo runs with S=100, K=105, T=0.5yr, r=5%, σ=20% and prints prices, all Greeks, IV round-trip, and put-call parity residual for both call and put.

API

const { price, greeks, impliedVol } = require('./blackScholes');

price(S, K, T, r, sigma, type)      // 'call' | 'put' — returns premium
greeks(S, K, T, r, sigma, type)     // returns { delta, gamma, theta, vega, rho }
impliedVol(marketPrice, S, K, T, r, type)  // returns IV (decimal) or null

Exported Functions

Function Description
price Black-Scholes premium for a European call or put
greeks All five Greeks in one call
impliedVol Bisection IV solver; returns null if not found within tolerance
normCdf Cumulative standard normal CDF
normPdf Standard normal PDF

Practice Ideas

  • Build an options chain by mapping price and greeks over a range of strikes
  • Plot the IV smile by solving impliedVol against market quotes at different strikes
  • Add a Newton-Raphson IV solver using vega and compare convergence speed

Next Steps

  • See the Python equivalent in Black-Scholes Option Pricing/
  • Combine with Monte Carlo Simulation - JavaScript/ to price path-dependent options
  • Explore Options Strategies/ for multi-leg payoff construction

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