Delta

Perhaps the most obvious risk an option trader faces is being exposed to movements in the underlying asset. The effect that a given movement in the price of the underlying asset has on an option’s price is known as the option’s Delta, and its value depends on the direction and the extent of the movement observed. It is calculated as follows:

Delta = Change in Option Value / Change in Underlying Asset Price

A helpful interpretation of Delta, or the option’s sensitivity to changes in the price of the underlying, is that it reflects the probability of the option being exercised. While this may indeed be a useful idea, especially for standard options, it is not exactly true, since the Delta of some exotic options can be significantly greater than one. Also, for forex options, the underlying currency exchange rate can pertain to a forward, spot or futures contract, depending on what forex option style is involved.

Furthermore, an option’s sensitivity to the underlying can be either positive or negative depending on whether the option involved is a put or call, and whether one is long or short the option. Generally, if your trading portfolio is long options, then any loss experienced with movements in the underlying is limited. On the other hand, if your trading portfolio is short options, then your losses are potentially unlimited.

Currency option market-makers managing a large portfolio of options in a particular currency pair must therefore be aware of the net Deltas of their portfolio of options so that they can quickly estimate their portfolio value’s sensitivity to movements in the underlying exchange rate, and hedge it if necessary.

For example, if the net Delta of a portfolio of AUD/USD options obtained by summing up all of the Deltas of the individual options contained within it weighted by their position size is +AUD1,000,000, then AUD1,000,000 would need to be sold versus the U.S. Dollar to immunize that particular portfolio against movements in the value of the underlying AUD/USD exchange rate.

This hedging process, and any subsequent rebalancing that is necessary to keep the portfolio neutral with respect to movements in the underlying is known as Delta hedging, and the resulting balanced portfolio is commonly referred to as a Delta-neutral portfolio.

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