Gamma

This is the rate at which the delta value of an option increases or decreases as a result of a move in the price of the underlying instrument.

Change in an option delta
Gamma =-------------------------------------
Change in underlying price

For example, if a Call option has a delta of 0.50 and a gamma of 0.05, then a rise of ±1 in the underlying means the delta will move to 0.55 for a price rise and 0.45 for a price fall. Gamma is rather like the rate of change in the speed of a car – its acceleration – in moving from a standstill, up to its cruising speed, and braking back to a standstill. Gamma is greatest for an ATM (at-the-money) option (cruising) and falls to zero as an option moves deeply ITM (in-the-money ) and OTM (out-of-the-money) (standstill).

If you are hedging a portfolio using the delta-hedge technique described under "Delta", then you will want to keep gamma as small as possible as the smaller it is the less often you will have to adjust the hedge to maintain a delta neutral position. If gamma is too large a small change in stock price could wreck your hedge. Adjusting gamma, however, can be tricky and is generally done using options -- unlike delta, it can't be done by buying or selling the underlying asset as the gamma of the underlying asset is, by definition, always zero so more or less of it won't affect the gamma of the total portfolio.

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