Calculate Delta, Gamma, Theta, Vega, Rho, theoretical price and implied volatility with the Black-Scholes model.
| Spot change | Spot | Option price | Delta | Gamma | Theta / day | Vega |
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Option Greeks measure how an option's price reacts to changes in the underlying price, time, volatility and interest rates. Delta is the sensitivity to the underlying price, Gamma is how fast Delta changes, Theta is the time decay per day, Vega is the sensitivity to implied volatility and Rho is the sensitivity to interest rates.
It uses the Black-Scholes model for European options. Enter the spot price, strike, days to expiry, interest rate and either the implied volatility or the option's market price. If you enter the market price, the calculator solves for the implied volatility first and then shows the Greeks. Theta is shown per calendar day, and Vega and Rho are shown for a 1% change.
Option sellers watch Theta and Vega to understand time decay and volatility risk, while option buyers watch Delta and Gamma to understand how quickly a position gains or loses as the index moves. The table below the results shows how price and Delta change as the spot price moves, so you can see the risk of a position before you trade.
Delta shows how much an option's price is expected to change for a 1 point move in the underlying. A call has a Delta between 0 and 1 and a put has a Delta between -1 and 0. Delta is also often read as a rough estimate of the probability that the option finishes in the money.
Theta is the amount an option's price is expected to fall each day because of time decay, with everything else unchanged. The calculator shows Theta per calendar day. Theta usually becomes larger as expiry gets closer for at-the-money options.
Implied volatility is the volatility that makes the Black-Scholes price equal to the option's market price. When you enter an option price, the calculator searches for that volatility numerically and uses it to compute the Greeks.
Use a short-term risk-free rate such as the government T-bill yield. For short-dated index options the rate has only a small effect on the result, so a rough value is usually enough.
Not always. Brokers and data vendors may use different models, interest rates, dividend assumptions and times to expiry, so small differences are normal. Treat the results as a close estimate.
Yes, you can enter any spot price, strike and expiry. The Black-Scholes model is an approximation, so results are most reliable for liquid, near-the-money options.
These tools are for educational and informational purposes only. Results are estimates based on the inputs and data shown, and OPIFY does not provide trading tips or investment advice.
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