Gamma Hedging

Gamma hedging is an options strategy designed to control the change in an option position’s delta as the underlying asset moves. Traders use it to reduce exposure to large or rapid price swings—especially near expiration—by keeping the portfolio’s rate of change of delta (gamma) near a desired level.

Key concepts

• Delta: the sensitivity of an option’s price to a small change in the underlying asset’s price (approximate change in option price per $1 move).
• Gamma: the rate at which delta itself changes for a $1 move in the underlying. Gamma measures the curvature (second-order sensitivity) of an option’s value relative to the underlying price.
• Gamma neutral: a portfolio whose net gamma is close to zero, so the portfolio’s delta changes little as the underlying moves.

How gamma hedging works

Gamma hedging typically involves adding option contracts (or adjusting strikes and positions) to offset the portfolio’s net gamma. Steps and ideas:

• Determine the portfolio’s current delta and gamma.
• Add or remove option positions (or adjust underlying holdings) to bring net gamma toward the target (often zero).
• Maintain or rebalance the delta hedge as the underlying moves—if gamma is neutral, delta will stay more stable and require fewer large adjustments.

Example: if a trader holds many long calls (positive gamma), they might sell a small number of calls at a different strike or buy puts to reduce gamma exposure and limit sharp option price moves from sudden underlying shifts.

Gamma hedging is calculation-intensive and requires frequent monitoring, especially when time to expiration is short (gamma typically rises as expiration approaches).

Gamma vs. Delta (simple illustration)

• If an option’s delta = 0.50 and gamma = 0.10:
• After a $1 rise in the underlying, delta ≈ 0.60 (0.50 + 0.10).
• For a $2 total move, approximate option price change ≈ first-dollar change (0.50) + second-dollar change (0.60) = 1.10.
• Delta measures first-order sensitivity; gamma captures how that sensitivity itself changes with the underlying.

Delta–Gamma hedging

Delta–gamma hedging combines both hedges:

• Delta hedge: neutralizes immediate (first-order) exposure by trading the underlying (or using offsets).
• Gamma hedge: limits changes in delta so the delta hedge remains effective across larger moves.
• In practice, traders set a target net gamma (often zero) and then adjust underlying holdings to achieve the desired delta. Rebalancing frequency depends on realized moves, time to expiration, and transaction costs.

Note: A trader can choose to be gamma neutral while retaining a net positive or negative delta if they wish to maintain directional exposure.

When to use gamma hedging (trade-offs)

Advantages:
* Reduces vulnerability to large, rapid moves in the underlying.
* Helps stabilize delta hedges and lower the need for disruptive rebalancing near expiration.

Drawbacks and costs:
* Requires adding option positions or frequent rebalancing, increasing transaction costs.
* Managing gamma can increase trading activity and margin requirements.
* Perfect hedging is costly and rarely permanent; portfolios must be monitored and adjusted as market conditions and Greeks change.

Takeaways

• Gamma hedging manages second-order option risk—how delta changes as the underlying moves.
• It is typically used alongside delta hedging to keep a position stable across both small and large price changes.
• Gamma hedging is most relevant when time to expiration is short or when rapid price movements are expected, but it involves trade-offs in cost and complexity.