Gamma Hedging

What Is Gamma Hedging?

Gamma hedging is a trading strategy that tries to maintain a constant delta in an options position, often one that is delta-neutral, as the underlying asset changes price. It is used to reduce the risk created when the underlying security makes strong up or down moves, particularly during the last days before expiration.

An option position's gamma is the rate of change in its delta for every 1-point move in the underlying asset's price. Gamma is an important measure of the convexity of a derivative's value, in relation to the underlying asset. A delta hedge strategy, in comparison, only reduces the effect of relatively small underlying price changes on the options price.

How Gamma Hedging Works

A gamma neutral options position is one that has been immunized to large moves in an underlying security. Achieving a gamma neutral position is a method of managing risk in options trading by establishing an asset portfolio whose delta's rate of change is close to zero, even as the underlying rises or falls. This is known as gamma hedging. A gamma-neutral portfolio is thus hedged against second-order time price sensitivity.

Gamma hedging consists of adding additional option contracts to a portfolio, usually in contrast to the current position. For example, if a large number of calls were being held in a position, then a trader might add a small put-option position to offset an unexpected drop in price during the next 24 to 48 hours, or sell a carefully chosen number of call options at a different strike price. Gamma hedging is a sophisticated activity that requires careful calculation in order to be done correctly.

Gamma vs. Delta

Gamma is the Greek-alphabet inspired name of a standard variable from the Black-Scholes Model, the first formula recognized as a standard for pricing options. Within this formula are two particular variables that help traders understand the way option prices change in relation to the price moves of the underlying security: delta and gamma.

Delta tells a trader how much an option's price is expected to change because of a small change in the underlying stock or asset — specifically a one-dollar change in price.

Gamma refers to the rate of change of an option's delta with respect to the change in price of an underlying stock or other asset's price. Essentially, gamma is the rate of change of the rate of change of the price of an option. However, some traders also think of gamma as the expected change resulting from the second consecutive one-dollar change in the price of the underlying. So that by adding gamma and delta to the original delta, you'd get the expected move from a two dollar move in the underlying security.

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 also in the delta itself — as the underlying asset moves. With delta hedging alone, a position has protection from small changes in the underlying asset. However, large changes will change the hedge (change the delta), leaving the position vulnerable. By adding a gamma hedge, the delta hedge remains intact.

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 underlying 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.

A trader who is trying to be delta-hedged or delta-neutral is usually making a trade that has very little change based on the short-term price fluctuation of a smaller magnitude. Such a trade is often a bet that volatility, or in other words, demand for the options of that security, will trend towards a significant rise or fall in the future. But even delta hedging will not protect an options trader very well on the day before expiration. On this day, because so little time remains before expiration, the impact of even a normal price fluctuation in the underlying security can cause very significant price changes in the option. Delta hedging is therefore not enough under these circumstances.

Gamma hedging is added to a delta-hedged strategy as a way of protecting the trader from larger than expected changes to a security, or even an entire portfolio, but most often to protect from the effects of rapid price change in the option when time value has almost completely eroded.

While many times a trader will seek a delta-gamma hedge that is delta-neutral; alternatively, a trader may want to maintain a specific delta position, which could be delta positive (or negative) but at the same time gamma neutral.

Gamma Hedging vs. Delta Hedging

As we have seen above, delta- and gamma-hedging are often used together. A simple delta hedge can be created by purchasing call options, and shorting a certain number of shares of the underlying stock at the same time. If the stock's price remains the same, but volatility rises, the trader may profit unless time value erosion destroys those profits. A trader could add a short call with a different strike price to the strategy to offset time value decay and protect against a large move in delta; adding that second call to the position is a gamma hedge.

As the underlying stock rises and falls in value, an investor may buy or sell shares in the stock if she wishes to keep the position neutral. This can increase the trade's volatility and costs. Delta and gamma hedging don't have to be completely neutral, and traders may adjust how much positive or negative gamma they are exposed to over time.