Options Pricing Calculator (Black-Scholes)

A mathematical model that estimates an option's theoretical value from the underlying price, strike, time to expiration, volatility, and interest rates. It assumes constant volatility and lognormal price movement: a useful baseline for fair value, not a prediction of where the option will trade.

Delta, gamma, theta, vega, and rho measure how the option's price responds to changes in the underlying, volatility, time, and interest rates. Delta is the headline figure: roughly how much the option moves for a $1 move in the stock. Theta is the daily cost of holding as expiration approaches.

Because implied volatility is not constant and markets price in events, skew, and supply and demand that the model ignores. The gap between model value and market price is often where the interesting information is — it tells you what volatility assumption the market is using.

Use implied volatility from the option's market price when checking fair value, or a historical estimate when scenario-testing. Small volatility changes move long-dated options a lot, so test a range rather than trusting a single input.

Strictly it is a European-exercise model. For American options it remains a good approximation except where early exercise matters: deep in-the-money puts and calls around ex-dividend dates.