Negative Gamma Strategies

Introduction

In the realm of options trading, gamma is a crucial risk metric that measures the rate of change of delta in an option relative to changes in the price of the underlying asset. Delta represents the sensitivity of the option’s price to movements in the price of the underlying asset. Gamma, therefore, provides insight into the convexity or curvature of the option’s payoff profile.

Negative gamma refers to a situation where the gamma of an options position is negative, meaning that the position loses delta faster than it gains it when the price of the underlying asset moves. This characteristic can lead to greater risks in volatile markets but can also be harnessed by sophisticated traders through targeted strategies known as negative gamma strategies.

Understanding Gamma

Definition of Gamma

Gamma (Γ) is the second derivative of an option’s price with respect to the price of the underlying asset. Mathematically:

[ [Gamma](../g/gamma.html) = \frac{\partial^2 V}{\partial S^2} ]

where ( V ) is the price of the option, and ( S ) is the price of the underlying asset.

Interpretation of Gamma

• Positive Gamma: Implies that as the underlying asset’s price increases, the delta of the option increases. Conversely, as the underlying asset’s price decreases, the delta of the option decreases.
• Negative Gamma: Implies that as the underlying asset’s price increases, the delta of the option decreases. Conversely, as the underlying asset’s price decreases, the delta of the option increases.

Positive gamma is typically found in long options positions (both calls and puts), whereas negative gamma is associated with short options positions.

Negative Gamma Strategies

Negative gamma strategies capitalize on the unique attributes of negative gamma positions, typically through options writing (selling) strategies. These strategies are designed to benefit from periods of low volatility, where the underlying asset’s price remains relatively stable.

Types of Negative Gamma Strategies

1. Short Straddle

A short straddle involves selling both a call option and a put option with the same strike price and expiration date. This strategy profits from minimal movement in the underlying asset’s price, as the premiums collected from selling the options will exceed any losses if the price remains stable.

- **[Risk](../r/risk.html)/Reward Profile**: While the potential [profit](../p/profit.html) is limited to the premiums received, the [risk](../r/risk.html) can be substantial if the [underlying](../u/underlying.html) price moves significantly in either direction.
- **Example**: Selling a call and [put option](../p/put.html) on XYZ stock, both with a [strike price](../s/strike_price.html) of $100 and expiration in one month, aiming to [profit](../p/profit.html) from low [volatility](../v/volatility.html) in XYZ’s stock price.

1. Short Strangle

A short strangle involves selling an out-of-the-money call and an out-of-the-money put with different strike prices but the same expiration date. This strategy also benefits from low volatility, but it provides a larger range within which the underlying asset’s price can move without causing a loss.

- **[Risk](../r/risk.html)/Reward Profile**: Similar to a [short straddle](../s/short_straddle.html), but with a potentially wider [profit](../p/profit.html) [range](../r/range.html) and correspondingly lower premiums collected compared to a [straddle](../s/straddle.html).
- **Example**: Selling a [call option](../c/call_option.html) on XYZ stock with a [strike price](../s/strike_price.html) of $110 and a [put option](../p/put.html) with a [strike price](../s/strike_price.html) of $90, both expiring in one month.

1. Iron Condor

An iron condor involves selling an out-of-the-money call and an out-of-the-money put while simultaneously buying a further out-of-the-money call and a further out-of-the-money put. This creates a position with limited risk and limited profit potential, benefiting from low volatility in the underlying asset’s price.

- **[Risk](../r/risk.html)/Reward Profile**: The maximum [profit](../p/profit.html) is achieved if the [underlying](../u/underlying.html) price remains between the two strike prices of the sold [options](../o/options.html), with the maximum loss limited to the difference between the strike prices of the sold and bought [options](../o/options.html) minus the [net premium](../n/net_premium.html) received.
- **Example**: Selling a [call option](../c/call_option.html) on XYZ stock with a [strike price](../s/strike_price.html) of $105 and a [put option](../p/put.html) with a [strike price](../s/strike_price.html) of $95, while buying a [call option](../c/call_option.html) with a [strike price](../s/strike_price.html) of $110 and a put with a [strike price](../s/strike_price.html) of $90, all expiring in one month.

1. Short Call or Put Spread

A short call spread involves selling a call option and buying another call option with a higher strike price and the same expiration date. Similarly, a short put spread involves selling a put option and buying another put option with a lower strike price.

- **[Risk](../r/risk.html)/Reward Profile**: These [spreads](../s/spreads.html) limit both the potential [profit](../p/profit.html) and potential loss, making them a more controlled negative [gamma](../g/gamma.html) strategy compared to outright short [options](../o/options.html) positions.
- **Example**: Selling a [call option](../c/call_option.html) on XYZ stock with a [strike price](../s/strike_price.html) of $100 and buying a [call option](../c/call_option.html) with a [strike price](../s/strike_price.html) of $105, both expiring in one month.

Managing Risk in Negative Gamma Strategies

Negative gamma strategies inherently involve significant risks, particularly in volatile market conditions. Effective risk management techniques include:

• Diversification: Holding a broad range of positions across different assets and strike prices to mitigate the impact of adverse price movements.
• Dynamic Hedging: Actively adjusting the delta of the portfolio to maintain a desired exposure level. This involves buying or selling the underlying asset to counterbalance changes in delta resulting from movements in the asset’s price.
• Using Stop-Loss Orders: Placing stop-loss orders to automatically close out positions at predefined loss levels.
• Limiting Position Size: Ensuring that individual positions do not constitute a disproportionate share of the overall portfolio, thereby reducing the impact of any single adverse price move.

Real-World Applications

Market Makers

Market makers, such as Virtu Financial [https://www.virtu.com/] and Citadel Securities [https://www.citadelsecurities.com/], frequently employ negative gamma strategies. Their role in providing liquidity involves continuously quoting buy and sell prices, necessitating the writing of options and maintaining delta-neutral portfolios through active hedging.

Hedge Funds

Hedge funds specializing in volatility arbitrage, like those managed by AQR Capital Management [https://www.aqr.com/] and options-focused funds, often utilize negative gamma strategies to exploit differences between implied and realized volatility. These funds deploy sophisticated algorithms and risk management frameworks to capture premiums from writing options while controlling gamma exposure.

Proprietary Trading Firms

Proprietary trading firms, such as Jane Street [https://www.janestreet.com/] and DRW [https://drw.com/], leverage their advanced trading systems and large capital bases to implement negative gamma strategies effectively. These firms utilize high-frequency trading algorithms to dynamically hedge their gamma exposure in real-time.

Advanced Considerations

Volatility Skew

Understanding volatility skew, the pattern of varying implied volatility across different strike prices, is crucial for successfully implementing negative gamma strategies. Traders must consider how skewness affects option pricing and adjust their strategies to account for higher or lower premiums at different strikes.

Impact of Dividends and Corporate Actions

Dividends and other corporate actions can significantly influence the behavior of options and the underlying asset’s price. Traders must adjust their negative gamma strategies to account for these events, ensuring that the impact on delta and gamma is appropriately hedged.

Utilization of Exotic Options

Exotic options, such as binary options or barrier options, can be incorporated into negative gamma strategies to create more complex payoff profiles. These options provide additional flexibility in managing gamma exposure and tailoring risk-reward characteristics to specific market conditions.

Conclusion

Negative gamma strategies offer sophisticated traders opportunities to profit from periods of low volatility by writing options and managing their delta exposure dynamically. While these strategies carry substantial risk, especially in volatile markets, diligent risk management and an in-depth understanding of gamma behavior can lead to consistent profits. Advanced applications by market makers, hedge funds, and proprietary trading firms highlight the versatility and potential of negative gamma strategies in various trading environments.