Understanding the Impact of Expiry on Gamma in Options Trading

Gamma, denoted as ΓΔ, is a crucial concept in options trading, representing the rate of change of an options' delta with respect to changes in the underlying asset's price. Gamma measures the curvature of an option's price in response to changes in the underlying asset's price. As options approach their expiry date, the behavior of gamma exhibits significant changes, often leading to an increase in its value for the following reasons:

Delta Sensitivity

As an option neared its expiry, its delta becomes increasingly sensitive to changes in the underlying asset's price. This heightened sensitivity can be explained by the fact that small movements in the underlying asset can result in larger changes in the delta, thus leading to a higher gamma.

Time Decay (Theta)

Options experience a phenomenon called time decay, denoted as theta, which accelerates for at-the-money options as they approach their expiry. This acceleration can lead to a steeper change in delta when the underlying asset's price fluctuates. As time runs out, the probability distribution of the underlying price becomes more concentrated, increasing the potential for rapid changes in delta and consequently, higher gamma.

Volatility Effects

Implied volatility near expiry can increase significantly for at-the-money options, leading to more substantial price movements. This increased volatility contributes to higher gamma, as the market anticipates larger potential price swings.

Probability of Finishing In-the-Money

As expiry approaches, the likelihood of an option finishing in-the-money or out-of-the-money changes significantly. This increased sensitivity in delta is particularly pronounced for options that are close to being at-the-money, further driving up the value of gamma.

In summary, gamma increases as options approach expiry due to heightened sensitivity of delta to changes in the underlying asset's price, accelerated time decay, and changes in market perceptions of volatility and the likelihood of the option finishing in-the-money.

Price Dynamics Near Expiry

The price of an option is influenced by two primary factors: intrinsic value and time value. Intrinsic value is the difference between the strike price and the current market price of the underlying asset, while time value represents the potential of the option to move in favor of the holder. As an option approaches its expiry date, the time value converges to zero, and the option's price becomes solely determined by its intrinsic value.

For options traded at a high premium, the rate of change of delta may be high as the time period to expire rapidly decreases. This quick convergence to zero time period makes for large variations in gamma value, further highlighting the importance of understanding gamma in trading strategies.

Conclusion

Understanding the dynamics of gamma in relation to the expiry date of an option is essential for traders to manage risk and optimize their trading strategies. Whether you're a seasoned trader or a newcomer to options trading, grasping these concepts can significantly enhance your ability to navigate the complexities of the options market.