Can Option Gamma Be Negative?

Yes, option gamma can indeed be negative, but to fully grasp this concept, we must first dig into what gamma truly represents and its implications in options trading. Gamma is one of the key "Greeks" in options trading, and it measures the rate of change in an option's delta with respect to the underlying asset's price. Simply put, while delta measures how much an option's price is likely to change for each dollar the underlying stock moves, gamma indicates how quickly delta itself is changing.

A positive gamma is commonly seen when an option is in or near-the-money. When the gamma is positive, the delta increases as the price of the underlying asset rises, and decreases when the underlying price falls. This characteristic makes gamma an important measure for risk management, as it affects how responsive the option's price is to the movement of the underlying asset. On the flip side, a negative gamma occurs when the option is far out-of-the-money or deep in-the-money. In such cases, the option's delta decreases as the stock price rises and increases as the stock price falls, leading to negative gamma.

Key Scenario: Negative Gamma and Its Effects

If you're short on an option position, particularly short gamma, this introduces substantial risk. In a short gamma scenario, traders are exposed to significant volatility risks, which could lead to losing positions if not carefully managed. For instance, if you're short a call option with negative gamma, as the underlying asset price rises, your delta will increase at a slower pace, which might leave your short call position vulnerable to unlimited losses. This underscores why understanding gamma, and more specifically negative gamma, is crucial for traders who want to avoid being blindsided by sudden market moves.

Moreover, negative gamma is more prevalent in certain strategies, such as short straddles and short strangles, where the trader benefits from low volatility. However, if volatility increases, the trader faces the risk of significant losses due to the increased sensitivity of the option's price to movements in the underlying asset. In contrast, positive gamma is seen in long options positions, providing more safety since the delta increases with favorable movements in the underlying asset, limiting potential losses.

Here’s an example that might help illustrate these dynamics:

Stock Price	Option Type	Delta	Gamma
$50	Call (Long)	0.50	+0.10
$60	Call (Short)	-0.40	-0.08

Notice how the gamma decreases when the trader has a short call option? That's negative gamma at play. The short position leads to the delta changing in a way that works against the trader if the stock price rises, causing losses that can spiral out of control.

Digging Deeper: Mathematical Breakdown

The formula for gamma is the second derivative of the option price with respect to the price of the underlying asset. This second derivative reflects how the curvature of the price function changes as the stock price moves, providing insight into how the option will react to small changes in the underlying asset's price. This is crucial for understanding why gamma becomes negative in some cases, especially for deep in-the-money or far out-of-the-money options, where the probability of ending up in-the-money is low, resulting in a smaller delta change.

For example, for a call option:

• Gamma = ∂²Price / ∂Price² This means that gamma is essentially the rate at which delta itself changes. For options close to expiration or those with low implied volatility, gamma tends to be more extreme, either positive or negative, depending on the position.

Real-Life Trading Scenario:

Consider a trader who has written (sold) a large number of short call options. If the market becomes volatile, causing the underlying asset’s price to rise significantly, the trader’s delta becomes more negative, and the gamma further exacerbates this problem. This situation can lead to sudden, large losses, especially if the trader is not actively hedging their position.

Gamma scalping is a strategy employed by traders to manage their gamma exposure. Traders with a short gamma position may buy or sell the underlying asset to keep their delta neutral, thereby mitigating the risks associated with large market swings.

Conclusion

To summarize, yes, option gamma can be negative, and it plays a critical role in determining how your position reacts to price changes in the underlying asset. Negative gamma is more common in short options strategies or when the option is far out-of-the-money or deep in-the-money. For traders who understand how to manage gamma, particularly negative gamma, it can be a powerful tool for hedging and risk management. However, failing to consider gamma’s impact can expose you to significant risks, especially during periods of high volatility.

If you're dealing with options, knowing how to interpret and handle gamma is essential. Don't overlook its potential to either enhance or devastate your trading strategy, depending on whether you are long or short in the position.

Gamma may not be the most intuitive of the Greeks, but once understood, it becomes a vital metric for managing complex options positions. Stay on top of it, and you can navigate the volatile seas of options trading with more confidence and control.