Gamma is a measure that explains the sensitivity of an option’s delta value. We have already seen how delta can be explained as a thermometer that measures how ‘hot’ an option is. With the same analogy, gamma can explain how fast the temperature can shift, from freezing cold to boiling hot (or the other way around) when the stock price varies.
Gamma explains how much the option’s delta change when the underlying stock price changes with 1 unit. An option with a gamma of 0.033 and a delta of 0.5 will thus get a delta of 0.533 at the point the stock price goes up 1 unit.
Another expression for gamma is that it measures the lever of a position. It offers extended possibilities to compare the quality of different strategies. Two delta neutral positions can seem to be equally attractive at a first glance, but if the one has a gamma of 0.0022 and the other a gamma of 0.311 they will react radically differently on market movements. The higher gamma, the more the price of options will increase when the market moves.
An option’s gamma is always positive, but it always approaches zero for obvious plus or minus options. This is logical since the probability that these options on short notice should change substantially is relatively low, as their delta values are insensitive. Similarly, gamma is highest for pari options. For these options, only a marginal change in the stock price is needed for the options to turn plus or minus.
As the expiry day approaches, the value of the gamma data increases in value. Obvious plus or minus options have a gamma that sink towards zero the last days before expiration. Pari options however, have gamma values that formally sky rock the closer to expiration we get. The reason for this is the same as above: extremely little is needed for a pari option to turn into an obvious plus or minus option when it is time for settlement.
Just as investor can insure his portfolio against small price movements by making it delta neutral, so a portfolio can be insured by making it gamma neutral. The approach is the same: one can buy, sell or write options that, together with an existing portfolio, give a gamma that amounts to zero. Indeed, theoretically a portfolio that is both gamma and delta neutral is even insured against relatively large movements in the stock price.
