Delta-Gamma Hedging

Delta-gamma hedging is an options strategy that combines both delta and gamma hedges to mitigate the risk of changes in the underlying asset and in delta itself.

In options, delta refers to a change in the price of an options contract per change in the price of the underlying asset. In this sense, it is a derivative of price action. Gamma refers to the rate of change of delta, so it is a second derivative of price action.

Both help to gauge movement in an option’s price relative to how in-the-money or out-of-the-money the option is. Investors use a gamma hedge to protect themselves from the remaining exposure created through the use of a delta hedge, which is generated because delta hedges are more effective when the underlying asset has a single price.

Delta hedging aims to reduce, or hedge, the risk associated with price movements in the underlying asset by offsetting long and short positions. For example, a long call position may be delta-hedged by shorting the underlying stock. This strategy is based on the change in premium, or price of option, caused by a change in the price of the underlying security.

Delta itself measures the theoretical change in premium for each basis point or $1 change in price of the underlying.

Gamma hedging attempts to reduce, or eliminate, the risk created by changes in an option's delta.

Gamma itself refers to the rate of change of an option's delta with respect to the change in price of the underlying asset. Essentially, gamma is the rate of change of the rate of change of the price of an option. A trader who is trying to be delta-hedged or delta-neutral is usually making a trade that volatility will rise or fall in the future. Gamma hedging is added to a delta-hedged strategy to try and protect a trader from larger changes in the portfolio than expected or time value erosion.

With delta hedging alone, a position has protection from small changes in the underlying asset. However, large changes will change the hedge (change delta) leaving the position vulnerable. By adding a gamma hedge, the position freezes its delta so that the delta hedge remains intact and protective.

A delta-gamma hedge requires the purchase of an underlying asset, typically shares of stock, and a call option, while selling a call option at another strike price. The goal of the hedge is to eliminate both gamma and delta for the shares. The delta option component involves selling options to produce a negative delta.

Using a gamma hedge in conjunction with a delta hedge requires an investor to create new hedges when the underlying asset’s delta changes. The number of shares that are bought or sold under a delta-gamma hedge depends on whether the underlying asset price is increasing or decreasing, and by how much.

Large hedges that involve buying or selling significant quantities of shares and options may have the effect of changing the price of the underlying asset on the market, requiring the investor to constantly and dynamically create hedges for a portfolio to take into account greater fluctuations in prices.