Black-Scholes Option Pricing Calculator
Calculate theoretical call and put option prices using the Black-Scholes formula.
Theoretical Call Price$10.45
Theoretical Put Price$5.57
d10.35
d20.15
Understanding Black-Scholes
The Black-Scholes model is a mathematical model for pricing an options contract. In particular, the model estimates the variation over time of financial instruments, and using the implied volatility of the underlying asset derives the theoretical price of European call and put options.
The Variables
- Stock Price (S): Current market price of the underlying asset.
- Strike Price (K): The price at which the option can be exercised.
- Time to Maturity (T): Time until expiration, expressed in years.
- Risk-Free Rate (r): The theoretical rate of return of an investment with zero risk.
- Volatility (v): The standard deviation of the stock's returns.
Worked Example
- Stock Price: $100
- Strike Price: $100
- Time: 1 Year
- Rate: 5%
- Volatility: 20%
- Resulting Call Price: ~$10.45
- Resulting Put Price: ~$5.57
Frequently Asked Questions
Does Black-Scholes work for American options?
No, the standard Black-Scholes model assumes the option can only be exercised on the expiration date (European style). American options can be exercised early, making them slightly more valuable.