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A mathematical model that estimates the theoretical price of a European option from stock price, strike, time, volatility, and interest rate.
Why It Matters
Black-Scholes is the foundation of modern options pricing. Every options chain you read, every Greeks number your broker shows, traces back to it (or a close cousin). It is not a perfect predictor — it assumes constant volatility and no early exercise — but it is the industry's shared reference for what an option is mathematically worth.
Key Points
- Inputs: stock price, strike, time to expiration, volatility, risk-free rate
- Outputs: theoretical price plus delta, gamma, theta, vega, rho
- Designed for European options; US equity options are American but trade close to Black-Scholes values
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Common Questions
A mathematical model that estimates the theoretical price of a European option from stock price, strike, time, volatility, and interest rate. Black-Scholes is the foundation of modern options pricing. Every options chain you read, every Greeks number your broker shows, traces back to it (or a close cousin).
Black-Scholes is the foundation of modern options pricing. Every options chain you read, every Greeks number your broker shows, traces back to it (or a close cousin). It is not a perfect predictor — it assumes constant volatility and no early exercise — but it is the industry's shared reference for what an option is mathematically worth.
Inputs: stock price, strike, time to expiration, volatility, risk-free rate
Outputs: theoretical price plus delta, gamma, theta, vega, rho
Designed for European options; US equity options are American but trade close to Black-Scholes values