Options Greeks & Implied Volatility Calculator

Option Greeks are measures of how sensitive an option's theoretical price is to changes in the things that affect it: the underlying's price, time passing, volatility and interest rates. Each Greek isolates one of those sensitivities so you can see which factor is driving an option's value at a given moment.

Delta is how much an option's price moves for a ₹1 move in the underlying. A call's delta runs from 0 to 1, a put's from -1 to 0. It's also commonly used as a rough estimate of the probability the option expires in the money.

Gamma is how fast Delta itself changes as the underlying moves. It's highest for at-the-money options close to expiry, which is why short-dated ATM options can swing in value so quickly on small underlying moves.

Theta is how much value an option loses purely from one day passing, with everything else held constant. It's usually negative for a bought option, since time decay works against the buyer and in favor of the option writer.

Vega is how much an option's price changes for a 1 percentage-point change in implied volatility. Options with more time to expiry generally have higher vega, since there's more time for volatility to matter.

Implied volatility is the volatility figure that, plugged into Black-Scholes, reproduces the option's actual market price. It reflects what the market is currently pricing in, not a measurement of the past. Historical volatility, by contrast, is calculated directly from how much the underlying has actually moved over some prior period. The two often diverge, especially around earnings or other known events.

Yes, for exercise style specifically: both NSE index options and individual stock options are European-style, exercisable only at expiry, which is exactly what Black-Scholes assumes. This is a real distinction from many US-listed equity options, which are American-style and can be exercised early, making a plain Black-Scholes price a looser fit there. Note that single-stock options in India have been physically settled since October 2019 under a SEBI mandate, but that changes what happens at settlement, not the exercise style or the model's validity.

The yield on a Government of India Treasury Bill or G-Sec maturing close to the option's expiry is the standard proxy. For short-dated options, Greeks are far less sensitive to this input than to volatility, so a reasonable round figure is generally fine for estimation purposes.

It estimates what an option's theoretical price would become if the spot price, the number of days left and the volatility change, using the same Black-Scholes model. It is handy for planning an exit, for example to see how much time decay and a move in the underlying offset each other. The result is a model estimate, not a market quote, and it assumes the risk-free rate stays the same.