Black-Scholes calculator
| Greek | Call | Put | Meaning |
|---|---|---|---|
| Delta | 0.5494 | -0.4506 | per 1 move in the stock |
| Gamma | 0.0399 | 0.0399 | change in delta per 1 move |
| Vega | 0.1966 | 0.1966 | per 1 point of volatility |
| Theta | -0.0260 | -0.0178 | per day |
| Rho | 0.1248 | -0.1200 | per 1 point of rates |
d1 = 0.1241 · d2 = 0.0248 · N(d2) = 0.5099 (risk-neutral chance the call finishes in the money)
What the model does
Black-Scholes prices a European option from five inputs: the stock price, the strike, the time to expiry, the volatility and the interest rate (plus a dividend yield if there is one). Volatility is the only input you cannot observe, which is why traders quote options in implied volatility: the volatility that makes the model match the market price.
Reading the Greeks
Delta is how much the option moves when the stock moves by 1. Gamma is how fast delta changes. Vega is the change in price for a one-point change in volatility, and theta is what the option loses per day if nothing else moves. Rho is the sensitivity to a one-point change in rates.
An at-the-money call has a delta near 0.5, the largest gamma and vega for its expiry, and the fastest time decay. Change the inputs above and watch those relationships hold.
How this comes up in interviews
Trading interviews rarely ask you to recite the formula. They ask what happens to a call when volatility rises, why an American call on a stock without dividends is never exercised early, or how you would hedge a long straddle. Use the calculator to build that intuition, then test it.
Practise it
Frequently Asked Questions
Does this work for American options?
It prices European options. For an American call on a stock that pays no dividends the value is the same. American puts and calls on dividend-paying stocks can be worth slightly more.
What volatility should I enter?
Use the implied volatility quoted for that strike and expiry if you have it. Otherwise a recent realised volatility of the stock is a starting point.
Why is theta shown per day?
Traders think of time decay as what the position loses overnight. The figure is the yearly theta divided by 365.
More free tools: Expected value calculator · Kelly criterion calculator · Probability distribution calculator
For education and interview practice only. Not investment advice.