Delta Hedging and Gamma Hedging

Managing Your Option Risks

Delta hedging and Gamma hedging are strategies to reduce the risk of your option positions by creating offsetting positions in the underlying asset (usually the stock).

A. Delta Hedging: Staying Neutral to Small Price Changes

• What it is: A strategy to create a portfolio that is insensitive to small changes in the price of the underlying asset. You want your portfolio's value to remain relatively stable, regardless of minor stock price fluctuations.
• How it works:
  1. Calculate your portfolio's Delta: This is the sum of the Deltas of all your options and stock positions.
  2. Offset the Delta: If your portfolio has a positive Delta, you sell short shares of the underlying stock to create a negative Delta that cancels out the positive Delta. If your portfolio has a negative Delta, you buy shares of the underlying stock to create a positive Delta that cancels out the negative Delta.
  3. Rebalance Regularly: As the stock price changes, your option Deltas will also change (especially if Gamma is high). You need to rebalance your hedge by buying or selling more shares to maintain a Delta-neutral position.
• Example:
  • You own a call option with a Delta of 0.60 on 100 shares of stock (total Delta = 60).
  • To Delta hedge, you would short 60 shares of the stock.
  • If the stock price goes up slightly, your call option will increase in value, but your short stock position will lose a small amount of money. These gains and losses should roughly offset each other.
• Formula:
  • Number of shares to hedge = - Portfolio Delta
• Why it matters:
  • Reduces directional risk: You're not betting on the stock price going up or down (at least in the short term).
  • Allows you to profit from other factors: You can focus on profiting from changes in volatility (Vega) or time decay (Theta) without being overly concerned about small stock price movements.
• Limitations:
  • Delta hedging only works for small price changes.
  • It requires frequent rebalancing, which can incur transaction costs.
  • It doesn't eliminate all risk (Gamma risk remains).

B. Gamma Hedging: Protecting Against Delta Changes

• What it is: A strategy to reduce the risk that your Delta hedge will become ineffective due to changes in Gamma. In other words, you want to protect your portfolio from large, unexpected changes in the stock price that would cause your Delta to shift significantly.
• How it works:
  1. Calculate your portfolio's Gamma: This is the sum of the Gammas of all your options positions.
  2. Offset the Gamma: You typically use other options to offset the Gamma of your existing portfolio. This usually involves buying or selling options with opposite Gamma. Because Gamma is always (or almost always) positive, you can't eliminate Gamma with the underlying security.
  3. Rebalance Regularly: As with Delta hedging, you need to rebalance your Gamma hedge as market conditions change.
• Example:
  • You have a Delta-neutral portfolio with a high positive Gamma. This means your Delta hedge is very sensitive to changes in the stock price.
  • To Gamma hedge, you might sell options (calls or puts) that have negative Gamma (or lower positive Gamma) to reduce your overall portfolio Gamma.
• Why it matters:
  • Reduces the need for frequent rebalancing of your Delta hedge.
  • Protects against large, unexpected price swings.
• Limitations:
  • Gamma hedging is more complex and expensive than Delta hedging.
  • It often involves trading multiple options, which can increase transaction costs.
  • It introduces other risks, such as Vega risk (sensitivity to changes in volatility).

C. Combining Delta and Gamma Hedging

• The Goal: To create a portfolio that is both Delta-neutral and Gamma-neutral. This means your portfolio is relatively insensitive to both small and large price changes in the underlying asset.

• The Challenge: Achieving both Delta and Gamma neutrality simultaneously is difficult and requires careful management. You typically need to use a combination of stocks and options with different characteristics.

• The Trade-off: Reducing Delta and Gamma risk often increases exposure to other risks, such as Vega risk and Theta (time decay). You need to carefully weigh these trade-offs based on your investment objectives and risk tolerance. D. Important Considerations

• Transaction Costs: Frequent rebalancing can be expensive.

• Model Risk: The calculations of Delta and Gamma are based on models (like Black-Scholes) that make simplifying assumptions. These models may not perfectly reflect real-world market conditions.

• Liquidity: You need to be able to buy and sell the underlying asset and options easily and at reasonable prices.