Implied Volatility Calculator
Reverse-engineer implied volatility from a market option price using Black-Scholes and Newton-Raphson.
For calls and puts on non-dividend-paying stocks.
Implied volatility (IV) is the market’s consensus estimate of how much a stock will move between now and option expiry. It is the single number you need to plug into the Black-Scholes formula to reproduce the observed market price. Every other input — stock price, strike, expiry, risk-free rate — is known. IV is what you solve for.
This calculator uses Newton-Raphson iteration. Start with a guess of 30% annualized volatility, compute the Black-Scholes price, compare to the market price, and adjust. The key insight: the derivative of option price with respect to volatility (called “vega”) tells you exactly how large to make each adjustment. The iteration typically converges in under ten steps.
The Black-Scholes formula for a call: C = S·N(d1) - K·e^(-rT)·N(d2) where d1 = [ln(S/K) + (r + σ²/2)T] / (σ√T) and d2 = d1 - σ√T.
For a put: P = K·e^(-rT)·N(-d2) - S·N(-d1)
Vega (same for calls and puts): S·√T·n(d1), where n is the standard normal PDF.
IV reflects what traders expect, not what a pricing model predicts. High IV means the market is pricing in big moves — often ahead of earnings or macro events. Low IV means complacency. Comparing IV to historical volatility tells you whether options are cheap or expensive relative to recent price action.
The chart plots Black-Scholes option price versus volatility from 1% to 150%, so you can see where your market price sits on the curve.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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