Understanding Gamma
Of course the Greek values used in the course of option pricing can all be statistically graphed; however none is more useful in graphical format than the gamma of an option.
The gamma is the rate of change of an options delta, and will increase as the market approaches the strike price, and decrease as it moves away from it.
Given that the delta is the rate of change of an options price to a corresponding increment in the underlying, an options gamma is then found to be ‘the rate of change, of the rate of change’ of the options price to a corresponding increment in the underlying. As much an exercise in the ludicrous as this may appear, it is absolutely accurate in its assertion.
At-the-money options have a delta of 50%, and it is just such options that have the greatest rate of change of delta; the greatest gamma. Other options have a delta that changes also, but it is the at-the-money option that does so to the greatest extent.
Particularly when the competing interests of time decay and underlying market direction are being considered, it is often the case that one needs more or less as the case may be, of the rate of change of the options price to the incremental move in the underlying.
This is only possible with acquiring more gamma and directing these options and their characteristics into the portfolio. It is with the use of at-the-money options that this is most efficiently achieved, however it is also possible to choose alternative strike prices, although significant volume changes will need to be affected in order to meet the same ends.
For example, the gamma of an out-of-the-money option may be 0.0025. This means that the delta changes by 0.0025% for an increment in the underlying. An option with a delta of 17%, for a one point increment would increase its delta to 17.25% or 0.1725. With a four point move it will experience a change of 1% in delta. By comparison, an at-the-money option will have a delta of 50% and a larger gamma than the previous example say, 0.0045. For a one point move in the underlying, the options delta will change from 50% to 50.45% or 0.5045. With a four point move, this options delta will then experience a 1.8 % change in delta.
If resort to the out-of-the-money option is had, it will need a little less than double the amount of at-the-money options to achieve the same exposure. When portfolios need cover with expediency, it is with judicious use of at-the-money-options that the most effective strategy is achieved.
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