Volatility

CHAPTER 4The Basic Greeks: Gamma

Gamma describes how the delta of an option changes as the spot price moves. In practical option trading, it is commonly scaled to the change in the delta of an option in units of the base currency (EUR in the case of EUR‐USD or USD in the case of USD‐JPY, for example) for a 1% change in the spot rate. A gamma position of +10 million EUR loosely means that if EUR‐USD strengthens (weakens) by 1%, then the delta increases (decreases) by 10 million EUR.

The change in delta that results from gamma and a changing spot rate means that the trader must continually trade the underlying currencies in the market in order to remain delta hedged and hence insensitive to the direction in which spot moves. For a EUR‐USD option, if the gamma position is +10 million EUR, then by the time EUR‐USD spot has moved 1% higher, the trader must have sold 10 million EUR in order to be delta hedged.

It is intriguing to note that while a spot trader typically trades when he has a view on the direction in which spot will move next, an option trader who is delta hedging her gamma position trades spot in order not to take a view on the next movement of spot! Recall from Section 2.4 that after the trader executes the delta hedge, she is indifferent as to the direction in which spot moves.

Option traders often refer to options that expire in (approximately) one month or less as gamma contracts. In Chapter 1, I described how the buyer (seller) of a call or put option is said to ...