Black-Scholes pricer

How it works

The Black-Scholes model values the option as the expected payoff at expiry under a lognormal price, discounted at the interest rate, with the dividend yield taken off the drift. Delta is the change in the option's value for a 1 move in the underlying; gamma the change in delta for that move; vega the change in value for 1 point of volatility; theta the change in value as one calendar day passes; rho the change for 1 point of interest rate. The chart shows the chosen measure across prices of the underlying, today (solid) and, for the value, at expiry (dashed).

Assumptions

European exercise only, a constant volatility and interest rate, a continuous dividend yield, no fees or taxes, and prices that move without jumps. Listed options trade on each strike's own implied volatility, so market prices differ. For learning, not for pricing trades.

For information and education only. Not investment advice.