Gamma Hedging

Gamma hedging is a risk management strategy used by options traders to protect against changes in the delta of options positions. It involves adjusting a portfolio to account for the rate of change of the option’s delta, providing a better alignment with the underlying asset’s movements.

Understanding Gamma Hedging

Definition

Gamma hedging is designed to mitigate the risk associated with the second derivative of an option’s price in regard to the price of the underlying asset, known as gamma. When the price of the underlying asset changes, the delta (the first derivative) of an option also changes, and gamma measures that rate of change.

Key Components of Gamma Hedging

• Options Delta: Represents the sensitivity of the option’s price to changes in the price of the underlying asset. A higher delta indicates a greater sensitivity.
• Options Gamma: Measures the rate of change of delta relative to changes in the underlying asset’s price. High gamma values indicate that the delta will change significantly with small price movements in the underlying asset.
• Underlying Asset: The financial instrument (stocks, ETFs, etc.) upon which an option is based.

How to Execute Gamma Hedging

1. Identify the Position: Analyze your current options position to determine its delta and gamma.
2. Calculate the Required Hedge: Determine the hedge ratio, which is the amount of the underlying asset needed to offset the changes in delta.
3. Adjust the Position: Buy or sell the underlying asset to create a delta-neutral position.
4. Monitor Portfolio: Continuously monitor the gamma and adjust the hedge as needed since market conditions and delta will change over time.

Real-World Example of Gamma Hedging

Suppose an investor holds a call option with a delta of 0.5 and a gamma of 0.1. If the underlying stock price increases, the delta will increase, potentially exposing the investor to undesired risk.

1. If the underlying asset price rises by $1, the new delta would become 0.6 (0.5 + 0.1).
2. To remain gamma-neutral, the investor would need to sell a portion of the underlying shares equal to the increase in delta. For 100 options, this means selling 10 shares of the underlying asset.
3. By doing so, the investor can maintain a balanced position as the underlying asset price fluctuates.

Gamma hedging is particularly effective in volatile markets, where rapid price movements can lead to significant changes in delta, enabling traders and investors to manage their risk more effectively.