Introduction

In this chapter, we will explore the practical aspects of managing option positions by implementing and maintaining delta-neutral and gamma-neutral positions. These strategies are fundamental in risk management and aim to mitigate exposure to changes in the underlying asset’s price and volatility. Understanding how to balance delta and gamma enables traders and investors to fine-tune their positions for specific market conditions.

Delta-Neutral Positions

Implementing Delta-Neutral Positions

Delta-neutral positions are designed to minimize the sensitivity of an options portfolio to changes in the underlying asset’s price. To implement a delta-neutral position, you take actions that offset the delta of your options.

Example: Suppose you hold a portfolio of call options with a total delta of +0.70. To make this position delta-neutral, you can sell short 70 shares of the underlying asset. The negative delta from the short stock position offsets the positive delta from the call options.

Maintaining Delta-Neutral Positions

Maintaining delta neutrality is an ongoing process. As the underlying asset’s price changes, the delta of your options will change as well. To maintain delta neutrality, you must adjust your position by buying or selling options or the underlying asset.

Example: If the underlying asset’s price increases, the call options’ delta becomes more positive. To re-establish delta neutrality, you might sell some of the call options.

Gamma-Neutral Positions

Implementing Gamma-Neutral Positions

Gamma-neutral positions are designed to minimize the sensitivity of an options portfolio to changes in the underlying asset’s volatility. To implement a gamma-neutral position, you aim to balance positive and negative gamma.

Example: Suppose you have a portfolio with a positive gamma of +0.05. To make this position gamma-neutral, you can add options with a negative gamma of -0.05. This offsets the gamma, making your position less sensitive to changes in volatility.

Maintaining Gamma-Neutral Positions

Maintaining gamma neutrality requires constant vigilance. As market conditions change, your portfolio’s gamma will fluctuate. You may need to adjust your position by buying or selling options to maintain gamma neutrality.