The option Greeks

Why the Greeks exist

An option’s premium changes for several reasons at once: the price of the index or share moves, time passes, and the market’s expectation of future swings changes. The Greeks are measures, named mostly after Greek letters, that separate these effects. They come from a pricing model, usually Black-Scholes, so they are estimates, not guarantees.

Delta

Delta is how much the option’s price is expected to change for a ₹1 move in the underlying price. Call deltas run from 0 to 1 and put deltas from 0 to −1. An at-the-money option has a delta near 0.5 (or −0.5 for a put). Deep in-the-money options have deltas near 1, and far out-of-the-money options near 0.

Gamma

Gamma is how much delta itself changes for a ₹1 move in the underlying. It is highest for at-the-money options and rises sharply as expiry gets close. High gamma means the option’s price can change quickly with small moves in the underlying.

Theta

Theta is how much the option’s price is expected to fall with one day’s passing, other things staying the same. It is usually shown as a negative number for option buyers. Time decay tends to speed up in the last days before expiry, especially for at-the-money options.

Vega

Vega is how much the option’s price is expected to change for a one percentage point change in implied volatility. Options with more time to expiry have higher vega. Both calls and puts gain value when implied volatility rises, other things staying the same.

Rho

Rho is how much the option’s price is expected to change for a one percentage point change in interest rates. For short-dated index options it is usually small compared with the other Greeks.

Implied volatility (IV)

Implied volatility is the level of future price swings that, when put into the pricing model, gives the option’s current market price. It is worked backwards from the price, so it reflects what buyers and sellers are paying, not a forecast of what will happen. It is quoted as a yearly percentage.

IV usually differs from strike to strike and from expiry to expiry. India VIX is an index worked out by NSE from Nifty option prices, and it summarises expected volatility over the next 30 days.

Limits of the Greeks

Each Greek assumes only one thing changes at a time. In real markets, price, time and volatility all move together, and models assume things (such as smooth price moves) that do not always hold. The Greeks describe sensitivity; they do not say what will happen.