What is option gamma?
By Simon Gleadall, CEO of Volcube.
The value of an option is affected by changes in the price of the underlying product. For example, the value of calls and puts on say gold typically vary when the price of gold varies. Now the amount by which the options vary for a change in the price of the spot product is revealed by the option delta. A delta of 1 (or 100%) means the option value changes 1 for 1 when the spot product price moves; gold moves up $1, the call option with a 100% delta will also increase in value by $1. A delta of say -0.5 (or -50%), such as an at-the-money put will have, means gold moving up $1 reduces the value of the put option by 50 cents.
But with options, things are rarely constant. The delta of an option is itself affected by the price movements in the underlying. This change in an option’s delta for a change in the price of the spot product is the option’s gamma. To make things easier, gamma is typically normalized so that it gives the change in delta for a 1 point change in the price of the undelying. For example, suppose a call option has a delta of 50%. It is an at-the-money call option (i.e. its strike price is equal to the spot price). Suppose that if the spot product rallies in price by $1, the call option’s delta increases to 57%. This indicates that the call option has 7 gamma.
Gamma is useful because it tells us by how much our portfolio’s overall delta will change if the spot price moves. Suppose we are pursuing a strategy that is delta-neutral. This means we are trying to maintain a delta of zero. Our gamma will tell us how we will need to re-hedge our portfolio if the spot price moves, in order to preserve delta neutrality. This is useful. contd below…
- Volume I – Option Gamma Trading
Option Gamma Trading (Volcube, 2013) – An accessible ebook guide to option gamma trading, from basic definitions to more advanced gamma hedging and gamma trading techniques as practised by professional option traders. Starting from first principles, option gamma is explained in straightforward English before separate sections on gamma hedging, gamma trading and advanced gamma trading […]
In fact, re-hedging a portfolio delta following a move in the spot price can have profit and loss implications. You can read more about gamma hedging here and about gamma trading here, which will explain this further. Gamma is additive across options of any duration (i.e. with any expiration date) that are struck on exactly the same underlying product. In other words, to find our total gamma exposure with respect to one product, we just add up the gamma from all our options struck on that product, regardless of the expiration date.
Gamma is the most important 2nd order option Greek. All options have positive gamma, whether they are put or calls. So to buy gamma, one buys options. Gamma varies depending on the strike of the options relative to the spot price, the level of implied volatility and the time remaining to expiration. Typically, gamma is higher in options nearest to being at-the-money, options closest to expiry in time and when implied volatility is low, other things being equal.
Volcube is an options education technology company, used by option traders around the world to practise and learn option trading techniques.