Gamma (Γ) is an options risk metric that describes the rate of change in an option’s delta per one-point move in the underlying asset’s price. Delta reflects how much an option’s premium (price) will change given a one-point move in the underlying asset’s price, making Gamma a measure of how the rate of change of an option’s price evolves with fluctuations in the underlying price. A higher Gamma indicates a more volatile option price.
Gamma is essential for assessing the convexity of a derivative’s value relative to the underlying asset. It is one of the ‘options Greeks’ alongside Delta, Rho, Theta, and Vega, all of which help evaluate the different types of risk in options portfolios.
Key Takeaways
- Gamma represents the rate of change for an option’s delta based on a single-point move in the delta’s price.
- It is a second-order risk factor, sometimes regarded as the delta of the delta.
- Gamma peaks when an option is at the money and is lowest when further away from the money.
- Highest Gamma is observed for options closer to expiration compared to far-dated ones.
- Gamma is utilized to gauge how movements in the underlying asset impact an option’s moneyness.
- Delta-gamma hedging helps in neutralizing an options position against underlying asset price movements.
Exploring the Essence of Gamma
Gamma is the first derivative of delta and indicates the price movement of an option relative to how much it is in-the-money or out-of-the-money. It measures how delta will shift as the underlying asset changes. For instance, if an option’s delta is +40 and the gamma is 10, a $1 increase in the underlying price will escalate the delta to +50.
Gamma is minimal when the option is considerably in- or out-of-the-money. However, it is largest when the option is near or at the money and typically peaks for options with near-term expirations compared to longer-dated options. Gamma is integral for hedging strategies by factoring in convexity, vital for substantial portfolio values needing precision, potentially applying third-order derivatives like ‘color’ for even more precise gamma measurement.
Practical Use of Gamma
Since the delta measure of an option is transient, Gamma provides traders with a more precise forecast of delta’s trajectory as the underlying price varies. Delta shows the option price change relative to the underlying asset’s price.
Gamma diminishes, nearing zero, as an option moves deeper into the money and delta approaches one, and similar performance is observed when diving out of the money. Gamma’s apex is when the price is at the money.
Consider the complex yet approximable calculation of gamma using financial software or spreadsheets. For example, for a call option on stock with a delta of 0.40, if the stock value increases by $1.00, the option will gain 40 cents, and delta shifts seemingly to 0.53—an approximate delta differential, yielding gamma. Options in long positions exhibit positive gamma, while short positions show negative gamma.
Real-world Example of Gamma
Imagine a stock trading at $10 with an option having a delta of 0.5 and a gamma of 0.10. For a $1 move in the stock price, the delta will adjust by 0.10. A $1 increase elevates delta to 0.60, whereas a $1 decrease dips delta to 0.40. This exemplifies Gamma’s differential impact.
How Traders Hedge Gamma
Gamma hedging aims for a constant delta in an options position, achieved by balancing bought and sold options, culminating in net gamma nearing zero or a gamma-neutral position. Traders often align zero-gamma around a delta-neutral position via delta-gamma hedging, neutralizing the options position value from underlying asset price alterations.
What Constitutes a Long Gamma Strategy?
Traders long gamma see their options position delta increase with underlying asset price movements. For instance, in a long gamma position, delta rises as the underlying price ascends and diminishes with falling prices. Selling deltas when prices rise and buying when they fall can inherently make long gamma positions profitable.
Understanding Gamma Risk
For short gamma positions, there is a compounded loss risk with underlying price movements. Starting delta-neutral, a rising stock increases short deltas, leading to increasing losses as ascension perseveres. Conversely, if deltas are procured at elevated prices and the asset price reverses, converting to long deltas, prior compounded losses magnify.
Final Thoughts
Gamma is an essential metric tracking the delta rate of change due to underlying asset price increments. It aids traders in anticipating delta dynamics for options or positions. Gamma is largest for at-the-money options, reducing for both in- and out-of-the-money positions. Importantly, for long positions in calls and puts, gamma remains invariably positive.
Investing, involving intricate elements like Gamma, demands an informed understanding of the underlying risk and potential for varying outcomes.
Related Terms: Delta, Theta, Vega, Options Greeks, Gamma Hedging.
References
- Sheldon Natenberg. **Option Volatility Trading Strategies. John Wiley & Sons, 2012.
