Gamma refers to the rate of change of delta of an options contract as compared to the change in the price of the underlying asset, therefore investors and traders try to use gamma hedging strategies to hedge their portfolio.
It measures the long-term price sensitivity of an underlying asset while delta measures the short-term price sensitivity. Gamma is also referred to as the second derivative of the price of a stock or asset.
Let us discuss what is Gamma, how Gamma hedging works, and its nuances.
What is gamma?
Gamma is the measure of the rate of change in delta for an option or any other financial security.
Gamma and other options Greeks like delta, theta, rho, etc. are widely used to measure different risks and price sensitivity of options.
Delta itself is the measure of change in the option’s price with a change to $1 in the underlying stock price.
Gamma value for long options will be positive and for short options will be negative. The Gamma values can range from –1 to +1 depending on the type of options contract.
Delta is the first derivative of the price of an option, whereas Gamma is the second derivative of the price of an option.
Gamma also measures the price sensitivity of an option with respect to the price change in the underlying stock. The difference between Gamma and Delta is the long-term and short-term price sensitivity measures for both these option Greeks respectively.
What is gamma hedging?
Since Gamma measures the rate of change of Delta, a Gamma hedging strategy would seek to keep Delta constant. Essentially, Gamma hedging is a risk management tool that keeps the impact of price changes of an underlying asset to a minimum on options’ prices.
Traders can use Gamma hedging in different ways. For instance, they can use sophisticated trading tools to select options and stocks in the portfolios to achieve delta-neutral positions.
Traders use delta hedging to reduce price sensitivity risks for options trading. However, delta hedging does not work when price changes are sudden and steep in either direction.
Therefore, traders use Gamma hedging methods to keep Delta stable. Since it measures the price sensitivity of options when price movements of an underlying asset are sharp, which can create extreme portfolio volatility.
How does gamma hedging work?
A common Gamma hedging strategy is to offset the options risk by taking oppositive positions. For instance, if you have a call option and the contract expiry is approaching, you can buy a put option or short the stock to minimize the delta sensitivity. It also allows traders to book some profits, if the cost of short exposure is less than the profits on the long.
Gamma score will be higher when options are at the money. The further the options diverge from this point the lower the Gamma score. It means Gamma will be at a minimum when options are in or out of the money.
Since long options have a positive Gamma (0 to +1), traders can take short options positions that will have a negative Gamma (-1 to 0).
Similarly, traders can take oppositive positions by going long or short with options and hedging by buying or shorting stocks.
Often traders want to achieve Gamma-neutral positions but keep a positive or negative delta. It means they can lock profits if they anticipate price movements in a specific direction of an underlying stock.
Achieving a Gamma-neutral position means having an overall zero Gamma for a portfolio or an options contract. At zero Gamma, the sensitivity of delta should also be constant.
Traders can take different options positions with long or short options to minimize the Gamma score. As a long position has a positive Gamma and a short position has a negative Gamma, therefore, a trader can offset the Gamma score by taking equal and opposite positions.
A closely linked strategy to hedge gamma is gamma-delta hedging. In practice, many traders use Gamma-Delta hedging to minimize the delta and gamma risks at the same time.
Delta hedging alone mitigates the risk of small price movements of options. However, gamma hedging is used to protect an investor against large and sudden price movements or even tail risks.
Therefore, when a trader uses both delta and gamma hedging, it achieves Gamma-Delta hedging.
Although a hedged position means zero delta or zero gamma score, it can also be achieved as a static score other than zero. For instance, a trader achieves a delta-neutral position but has a positive Gamma of +0.3.
Conversely, a trader may manage a portfolio with different options contracts having long and short options in a way that creates a Gamma-Neutral position while having a positive or negative delta overall.
What is the difference between delta and gamma hedging?
Delta hedging focuses on reducing the risks of sudden price movements in the underlying asset. Gamma on the other hand is related to how delta changes, based on the price fluctuation of the underlying asset, which measures how the price of options changes.
Delta hedging is used to prevent the risk of sudden underlying asset price movements. While gamma hedging protects large swings in the price of options.
How do market makers hedge gamma?
Depending on the strategy used a market maker may choose to hedge by buying the underlying asset or taking the same position.
For example, if a market maker sells a call option, they can hedge the gamma of that trade by buying the underlying asset or adding call options to their portfolio. This in part explains how gamma squeeze works.
How does a gamma squeeze work?
A gamma squeeze may happen when there is a large volume of call options. Since speculators are purchasing so many call options, market makers need to hedge their positions. This is done by buying additional call options or buying the underlying asset.
This forces the underlying asset price to go up, which in turn pushes the call options prices higher. Creating a positive feedback loop that can push prices extremely high.