Black-Scholes Option Pricing Calculator
This calculator helps finance professionals and students compute the theoretical price of European call and put options using the Black-Scholes model.
Calculator
Results
Data Source and Methodology
All calculations are based on the Black-Scholes model as described in academic and financial literature. Precise data can be found at MyStockOptions.
The Formula Explained
\( C = S_0 N(d_1) - X e^{-rT} N(d_2) \)
\( P = X e^{-rT} N(-d_2) - S_0 N(-d_1) \)
where \( d_1 = \frac{\ln(\frac{S_0}{X}) + (r + \frac{\sigma^2}{2})T}{\sigma \sqrt{T}} \)
and \( d_2 = d_1 - \sigma \sqrt{T} \)
Glossary of Terms
- Stock Price (S0): Current price of the underlying stock.
- Strike Price (X): The price at which the option can be exercised.
- Time to Maturity (T): Time in years until the option expires.
- Risk-Free Rate (r): The annualized risk-free interest rate.
- Volatility (σ): The annualized standard deviation of the stock's returns.
Frequently Asked Questions (FAQ)
What is the Black-Scholes model?
The Black-Scholes model is a mathematical model for pricing an options contract.
How do I interpret the results?
The calculated call and put prices represent the theoretical market price of the options.
Why is volatility important?
Volatility indicates the degree of variation of a trading price series over time.
Can I use this model for American options?
No, the Black-Scholes model is designed for European options, which can only be exercised at expiration.
What are the limitations of the Black-Scholes model?
The model assumes constant volatility and interest rates, which may not be realistic.
Formula (LaTeX) + variables + units
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\( C = S_0 N(d_1) - X e^{-rT} N(d_2) \) \( P = X e^{-rT} N(-d_2) - S_0 N(-d_1) \) where \( d_1 = \frac{\ln(\frac{S_0}{X}) + (r + \frac{\sigma^2}{2})T}{\sigma \sqrt{T}} \) and \( d_2 = d_1 - \sigma \sqrt{T} \)
- No variables provided in audit spec.
- MyStockOptions — mystockoptions.com · Accessed 2026-01-19
https://www.mystockoptions.com/black-scholes.cfm
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.