Calculator
Black–Scholes option calculator
The Black–Scholes–Merton model prices European options from five market inputs. It also gives the Greeks, which measure how the price responds to each input.
Option price
1.8376
- Delta
- 0.3287
- Gamma
- 0.04049
- Vega (per 1 vol pt)
- 0.1464
- Theta (per day)
- -0.0296
- Rho (per 1% rate)
- 0.0510
Formula
d₁ = [ln(S ÷ K) + (r − q + σ² ÷ 2) T] ÷ (σ √T), d₂ = d₁ − σ √T
Call = S e^(−qT) N(d₁) − K e^(−rT) N(d₂)
Put = K e^(−rT) N(−d₂) − S e^(−qT) N(−d₁)
How to use it
Enter spot, strike, days to expiry, the risk-free rate, dividend yield and volatility, and choose call or put.
Vega and rho are per 1 percentage-point move; theta is per calendar day.
Assumptions and limits
- European exercise only. American options on dividend-paying stocks can be worth more.
- Constant volatility and rates; real markets show a volatility smile.
Common questions
Which volatility should I use?
For valuing a traded option, use its implied volatility. For a theoretical value, many desks use a blend of implied and recent realised volatility.
Why is theta negative?
Long options lose time value as expiry approaches, all else equal. Deep in-the-money European puts can have positive theta.
For education only, not investment advice. Results depend entirely on the inputs and assumptions above; check important numbers independently.