Black-Scholes Calculator
Compute theoretical call or put option value using the Black-Scholes model with Greeks (Delta, Gamma, Theta, Vega, Rho).
Theoretical option price
12.0852
d1: 0.3050 | d2: 0.0550
Delta
0.6198
Gamma
0.0152
Theta / day
-0.0192
Vega / 1%
0.3808
Rho / 1%
0.4990
Expiry P/L preview (per 1 contract unit)
What is Black-Scholes?
The Black-Scholes model is a mathematical framework for pricing European options. It estimates fair value from spot price, strike price, time to expiration, risk-free rate, volatility, and dividend yield.
The model assumes lognormal asset returns, constant volatility, and frictionless markets. Real markets can deviate from these assumptions, so theoretical value and traded price may differ.
What the Greeks tell you
Delta
Price change for a 1-unit move in underlying.
Gamma
How fast Delta changes as price moves.
Theta
Time decay impact, often measured per day.
Vega and Rho
Sensitivity to volatility and interest rate shifts.
Interpretation guide
Use this model to benchmark option premium, compare strikes, and stress-test positions under volatility or rate changes.
Black-Scholes outputs are most aligned with European exercise style. American options with dividends may require different models for precision.
If market price is above model value, implied volatility may be elevated. If below, the market may be pricing lower future volatility or asymmetric risks.
Model assumptions vs market reality
Assumptions in model
- Constant volatility across time
- Continuous trading and no friction
- Lognormal price dynamics
- European exercise at expiry only
Reality in live markets
- Volatility smile and skew appear frequently
- Liquidity, spread, and slippage matter
- Jumps and regime shifts occur
- American exercise may affect fair value