Gamma - An Options Greek



Options trading may already be a part of your investing strategy. But whether you’ve been doing it for a while or are just getting started, it’s helpful to become proficient in the options concepts and lingo to be as successful as possible. Like any other investment strategy, options trading involves risks and they aren’t suited for everyone. So it’s important to fully grasp how options work, including the potential upsides and downsides. Understanding Gamma, along with the other Greeks, can help you do that and fine-tune your approach.


The Greeks are a way to measure the relative sensitivity of an option’s price to stock prices, market volatility, and timing. The option Greeks are Delta, Gamma, Vega, Rho, and Theta. Gamma is a popularly used Options Greek in the market.


Options Greek

Here’s a quick guide to the remaining option Greeks and what they measure:


Delta

An option’s delta refers to how sensitive the option’s price is, relative to a ₹ 1 change in the underlying security. Delta can be positive or negative, depending on if the option is a put or call.

Gamma

Gamma is a little different. It measures how sensitive the option’s delta is, relative to a ₹ 1 change in the underlying security. Gamma is used to track an option’s price movement to determine whether it’s in or out of the money.

Vega

Vega highlights how much an option’s contract price changes, relative to a 1% change in the underlying asset’s implied volatility. Essentially, it’s a way to gauge how much an option’s price could move up or down.


Rho

Rho (p) represents the rate of change between an option's value and a 1% change in the interest rate. This measures sensitivity to the interest rate. Rho measures the sensitivity of an option or options portfolio to a change in interest rate.

Theta

The option's theta is a measurement of the option's time decay. The theta measures the rate at which options lose their value, specifically the time value. In other words, theta addresses the inevitable loss in value that options experience as time passes. Theta is highest for at-the-money (ATM) options.


These option Greeks work together to help you devise a strategy for buying and selling options for maximum profit.


What is Gamma in trading?

Gamma is a term used in options trading to represent the rate of change in the option’s delta. While delta measures the rate of change in an option’s price compared to the underlying asset, gamma measures the rate of change in an option’s delta over time. In other words, Gamma is used to understand the change in delta, and to try and forecast future price movements in the underlying.


Gamma Behavior

Options with a high gamma will be more responsive to changes in the price of the underlying asset as compared to the options with a low gamma. In options trading, Gamma is always at its largest when an options contract is at the money because these options can quickly shift to being in the money or out of the money. Gamma is at its smallest when an options contract is comfortably in the money or out of the money because the likelihood of these options changing dramatically in value is greatly reduced. Gamma will always be positive for long options and it will always be negative for short options.


Since an option's delta measure is only valid for a short period of time, gamma gives traders a more precise picture of how the option's delta will change over time as the underlying price changes.


Example of gamma

Gamma is the rate of change in an option's delta per 1-point move in the underlying asset's price.

If a stock is trading at Rs.850 and there is an Out of the money (OTM) 870 call option that is quoting at Rs.18. Let us also assume that this stock has a delta of 0.4 (40%) and a gamma of 0.1 (10%). What happens when the stock price moves up from Rs.850 to Rs.880?


Since the delta is 0.4, the call option price will move up by 0.4 x (30) {Delta times change in the price of the underlying}. Thus the 870 call option price will move up by Rs.12 from Rs.18 to Rs.30. The delta will move up by the extent of the gamma in the above case. That is because the gamma measures the sensitivity of the delta to shifts in the stock price.


Gamma hedging strategy

A gamma hedging strategy can be used to reduce your exposure to risk in an options contract. You’d use it if the underlying market makes strong up or down moves contrary to your current options position, as the expiry date of the contract approaches.


For example, if you had a profitable position on a number of calls and the expiry date was approaching, you could take out a smaller position using put options. This would help to protect you against any unexpected price drops in the short time frame before the call options reached their expiry. You could do the same thing for a put option position. If the price of the put options you held had fallen below the strike price, meaning they’re profitable, you could take out a smaller call option position. This could help to protect you against any possible increases in price as the expiry date of the put options approaches.

What impacts the value of the gamma?

Like the value of the delta, the value of gamma is also dynamic and keeps changing over time. There are two factors that impact the value of the gamma over a period of time, viz. time to expiry and the volatility of the stock price. Let us understand this impact on the gamma.


As the time to expiration approaches, the gamma of the ATM option increases while the gamma of the OTM and the ITM options reduces. That is because there is greater scope for shifts in the delta in the ATM options compared to deep ITM and deep OTM options. There is another way to look at the impact of time to expiration and gamma values. Let us understand this by looking at 3 options with term to maturity of 1 month, 2 months, and 3 months respectively. What happens in each of these cases? While all the 3 will have a bell-shaped gamma curve, the bell curve will be sharpest in the case of the 1-month option and the flattest for the 3-month option. That is because there is greater visibility of change in delta in the 1-month option as compared to the 3-month option, which is still a bit hazy.


How will volatility impact gammas? Let us look at 2 situations where volatility is high and another situation where the volatility is low. How will the gamma curve look like? The gamma curve will be flat in case of high volatility and it will be sharp in case of low volatility. Why is this so? That is because when the volatility is high we already have a good degree of time value that is priced into the options. Hence the scope for changes in delta is quite limited making the gamma curve much flatter in times of high volatility.





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