Black–Scholes option pricing calculator
Price a European call or put under Black–Scholes–Merton and see how the value changes across a whole grid of spot prices and volatilities, not just at one point.
01 / DERIVATIVES
Options pricing
One model. A whole landscape of possibilities.
Read across for a change in spot. Read down for a change in volatility. Strike, time, rate and yield stay at your assumptions.
About this model +
Black–Scholes–Merton values European calls and puts with constant volatility, continuously compounded interest and a continuous dividend yield. It excludes fees, discrete dividends and early exercise. These are theoretical scenarios, not market quotes. At zero time the price equals payoff; at zero volatility it equals discounted deterministic payoff. Model reference ↗
How to use it
Set the strike, time to expiry, risk-free rate and dividend yield. The heatmap then shows the option value for each combination of spot (read across) and volatility (read down). Hover or focus a cell to inspect that scenario.
Switch to the payoff view to compare the model value today, the solid curve, with the exercise payoff at expiry, the dashed line. The gap between them is time value. The payoff excludes the premium you paid.
What it teaches
Calls gain value as spot rises and puts as it falls, and both gain value as volatility rises. The grid makes the curvature visible: value changes fastest near the strike, which is where gamma is largest.
Inputs are annualised on a 365-day year and prices are in USD per unit of the underlying. The model assumes constant volatility and continuous hedging, so treat the output as a model value, not a market quote.
Key formula
C = S·e^(−qT)·N(d₁) − K·e^(−rT)·N(d₂)
Learn the ideas behind it
- The Black–Scholes PDE, formula and implied volatility
- Greeks and numerical sensitivities
- No-arbitrage bounds and put–call parity