Understanding Gamma in Options Trading

Gamma is a critical measure in options trading, representing the rate of change in an option's delta relative to a $1 change in the price of the underlying asset. While delta measures the sensitivity of an option's price to changes in the underlying asset's price, gamma measures the sensitivity of delta itself to those changes. This makes gamma a second-order (acceleration) measure of an option's price sensitivity

Practical Example of Gamma

Consider a scenario where you hold a call option with a strike price of $35 on a stock currently trading at $35, making the option at-the-money. Assume the option has 20 days until expiration, an implied volatility of 30%, and an interest rate of 2.50%. If the option's premium is priced at $1.00, its delta might be 0.52, and its gamma could be 0.16.

This setup means if the stock's price rises by $1 to $36, the option's delta, originally at 0.52, suggests the option's price should increase to about $1.52. However, due to gamma, the actual price may end up slightly higher, say at $1.60. This occurs because delta itself increases as the stock price rises – from 0.52 at $35 to about 0.68 at $36, propelled by a gamma of 0.16.

Gamma Values

Gamma is always positive for both call and put options. This uniform positivity means that whether you hold a call or a put, the delta of your option becomes more sensitive as the underlying asset's price moves closer to the option's strike price. There's no upper limit to gamma, which can vary significantly based on the option's moneyness – its position relative to the strike price.

Gamma and Option Moneyness

At-the-Money: Gamma peaks when an option is at or near the money because it is at these points that small changes in the stock price can significantly impact the delta.
In-the-Money and Out-of-the-Money: Gamma decreases as options move deeper in or out of the money. Deep in-the-money options have deltas approaching 1 or -1, and their deltas change little with movements in the underlying price, leading to low gamma. Similarly, far out-of-the-money options, with deltas approaching zero, also exhibit low gamma.

Gamma Throughout Time

As options approach their expiration, the gamma of at-the-money options increases, making their delta more sensitive to changes in the underlying price. This heightened sensitivity can lead to larger changes in an option's price in response to movements in the underlying asset. Conversely, gamma decreases for both in-the-money and out-of-the-money options as they approach expiration.

Gamma and Volatility

Higher volatility generally increases gamma for out-of-the-money and in-the-money options, while reducing it for at-the-money options. This pattern reflects the increased uncertainty and potential for price movement away from the strike price.

Using Gamma in Trading

Understanding gamma helps traders manage the risk of large price swings in the underlying asset. It is particularly crucial in "delta-neutral" strategies like straddles, where the goal is to benefit from volatility rather than price direction. Such positions may have little initial delta, but high gamma can cause rapid changes in delta as the underlying price moves, potentially leading to significant profits or losses.

Summary

Gamma is a vital concept in options trading, enhancing our understanding of how an option's price sensitivity to the underlying asset can change. It is especially important for managing the risks associated with large price swings and for strategies that aim to capitalize on volatility. By keeping a close eye on gamma, alongside other Greeks like delta and theta, traders can more effectively tailor their strategies to changing market conditions and optimize their risk exposure