What Is Gamma?
Let me explain gamma to you directly: Gamma (Γ) is an options risk metric that shows how sensitive an option's delta is to changes in the underlying asset. It tells you how much the delta will shift when the underlying price moves by one point. So, gamma essentially measures how the rate of change in an option's price will adjust with fluctuations in the underlying price. If gamma is higher, the option's price becomes more volatile.
You should know that gamma captures the convexity of a derivative's value relative to the underlying asset. It's one of the 'options Greeks,' alongside delta, rho, theta, and vega, which help assess various risks in options portfolios.
Key Takeaways
- Gamma is the rate of change for an option's delta based on a single-point move in the underlying's price.
- It is a second-order risk factor, sometimes known as the delta of the delta.
- Gamma is at its highest when an option is at the money and is at its lowest when it is further away from the money.
- Gamma is also highest for options closer to expiration than farther-dated ones, all else equal.
- Gamma is used when trying to gauge how movements in the underlying asset will affect an option's moneyness.
- Delta-gamma hedging immunizes an options position against moves in the underlying asset.
Understanding Gamma
Gamma is always positive for long options and negative for short options. Think of it as the first derivative of delta; I use it to gauge an option's price movement relative to how in or out of the money it is. It shows how the delta changes as the underlying asset moves. For example, if an option's delta is +40 and gamma is 10, a $1 increase in the underlying price would push the delta to +50.
When the option is deep in or out of the money, gamma is small. But when it's near or at the money, gamma reaches its peak. Gamma is also larger for options with near-term expirations compared to longer-dated ones.
Gamma matters because it addresses convexity in hedging strategies. If you're managing large portfolios, you might need even more precision, and that's where a third-order derivative like 'color' comes in—it measures gamma's rate of change for maintaining gamma-hedged positions.
Fast Fact
As an analogy to physics, the delta of an option is its 'speed,' while the gamma of an option is its 'acceleration.'
What Is Gamma Used for?
Since an option's delta is only valid briefly, gamma gives you a more precise view of how the delta will evolve as the underlying price changes. Delta itself shows how much the option price shifts with the underlying asset's price.
Gamma decreases toward zero as an option goes deeper in the money, with delta approaching one. It also nears zero for deep out-of-the-money options. Gamma hits its highest when the price is at the money.
Calculating gamma is complex and usually requires financial software or spreadsheets for accuracy. But here's an approximation: Consider a call option with a delta of 0.40. If the stock rises by $1.00 and the delta becomes 0.53, the 0.13 difference is roughly gamma.
Important Note
All options in a long position have positive gamma, while all short options have negative gamma.
Example of Gamma
Suppose a stock trades at $10 with an option delta of 0.5 and gamma of 0.10. For every $1 move in the stock, the delta adjusts by 0.10. A $1 increase means the delta rises to 0.60; a $1 decrease drops it to 0.40.
How Do Traders Hedge Gamma?
Gamma hedging aims to keep a constant delta in an options position by buying and selling options to offset each other, targeting a net gamma near zero. This makes the position gamma-neutral. Often, you'll combine this with delta-neutral strategies via delta-gamma hedging, where both net delta and gamma are close to zero, immunizing the position against underlying price changes.
What Is a Long Gamma Strategy?
If you're long gamma, your position's delta increases with underlying price movements. For instance, in a long gamma setup, delta grows as prices rise or shrinks as they fall. This can profit you by selling deltas high and buying low.
What Is Gamma Risk?
For short gamma positions, there's risk of compounding losses from underlying price moves. Starting delta-neutral, a stock rise creates increasingly short deltas, leading to bigger losses if you buy deltas at higher prices, only for the asset to reverse and compound those losses on the way down.
The Bottom Line
Gamma measures the delta's rate of change per one-point increase in the underlying asset. It's a key tool for forecasting delta shifts in options or positions. Gamma is largest for at-the-money options and smaller for in- or out-of-the-money ones. Unlike delta, gamma is always positive for long calls and puts.
Remember, this information is general and doesn't consider your specific investment objectives, risk tolerance, or finances. Investing carries risks, including potential loss of principal.
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