Free Tool
Black-Scholes Calculator
Estimate the fair value of a call or put before expiration. Enter the underlying price, strike, time, volatility, and rates to get the theoretical price and every Greek — then watch how the value curve bends above intrinsic value as time and volatility change.
Call price
$3.02
$302.11 per contract
Put price
$2.69
$269.29 per contract
| Greek | Call | Put |
|---|---|---|
| DeltaPrice change per $1 move in the underlying | 0.5326 | -0.4674 |
| GammaDelta change per $1 move (same for call & put) | 0.0555 | 0.0555 |
| Theta / dayValue lost each calendar day | -0.0530 | -0.0421 |
| Vega / 1%Price change per 1 point of volatility | 0.1140 | 0.1140 |
| Rho / 1%Price change per 1% move in rates | 0.0413 | -0.0406 |
Value vs. underlying price
How to Use It
- 1. Enter the underlying and strike — the current stock price and the option’s strike.
- 2. Set time and volatility — days to expiry and the annualized volatility (a typical large-cap sits around 20–30%).
- 3. Add rates — the risk-free rate, and a dividend yield if the stock pays one.
- 4. Read the outputs — the call and put price, the Greeks table, and a value-vs-price chart you can switch between call and put.
The Formula
For a non-dividend or continuously-dividend-paying underlying, Black-Scholes-Merton prices are:
- 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)
Here S is the underlying price, K the strike, T the time to expiry in years, σ volatility, r the risk-free rate, q the dividend yield, and N() the standard normal distribution.
Frequently Asked Questions
What is the Black-Scholes model?
Black-Scholes is a formula for estimating the fair value of a European option before expiration. It combines the underlying price, strike, time to expiry, volatility, and interest rates into a single theoretical price, and is the foundation of modern options pricing.
What inputs does it need?
Underlying price, strike price, time to expiry (entered here in days), the annualized volatility of the stock, the risk-free interest rate, and — optionally — a continuous dividend yield. Volatility is the only input you cannot observe directly; it is an estimate of how much the stock will move.
What are the Greeks?
The Greeks measure how the option price responds to change. Delta is sensitivity to the stock price, gamma is how delta itself changes, theta is time decay per day, vega is sensitivity to volatility, and rho is sensitivity to interest rates. This calculator reports all five for both the call and the put.
How accurate is it for real options?
Black-Scholes assumes European exercise, constant volatility, and no early assignment, so it is a model, not a guarantee. Real listed options are usually American-style and trade at prices that reflect changing volatility. Use it to build intuition and compare scenarios, not as a precise market price.
Educational tool only. Black-Scholes is a theoretical model that assumes European exercise and constant volatility; real option prices differ. Nothing here is financial advice.