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The Complete Guide On Option Gamma

Option delta measures the sensitivity of the option price to changes in the price of the underlying asset. What does gamma measure? Gamma is another of the popularly used Options Greeks in the market. So, what is option gamma? Gamma is the second level measure and it measures the sensitivity of changes in delta to a unit change in the underlying stock price. We all know that delta is not static but it is a dynamic number. But how much does the delta change in response to stimuli like interest rates, volatility and time to expiry? That question is answered by Gamma.

Apart from understanding the concept of gamma, let us also apprehend option gamma trading and how to use gamma in option trading. While option gamma is a lot more complex compared to data, it is commonly used by options traders across the world.

Understanding all about gamma of options
Gamma represents the rate of change in the Delta for a unit price change in the underlying stock or index. Delta is a measure of the rate of change in the option premium whereas gamma measures the momentum. In other words, gamma measures movement risk. Like in the case of delta, the gamma value will also range between 0 and 1. Gammas are linked to whether your option is long or short in the market. So if you are long on a call option or long on a put option then your gamma will be positive. On the other hand, if you are short on a call option or short on a put option then your gamma will be negative.

Understanding gamma with an example
The gamma is normally the maximum when the strike price is very close to the stock price i.e. in case of ATM options. That is the time when the impact on the delta is the maximum. We may recall that delta shift the maximum when the options is ATM, slightly ITM and slightly OTM. As the options become very deep ITM or deep OTM, the impact on delta is minimal. Therefore, the gamma curve will reflect that. It will be more of a bell shaped curve where the gamma will be the maximum around the ATM options. As you go deep OTM or deep ITM, the bell curve starts becoming flat. Now for the example!

Let us assume that a stock is quoting at Rs.850 and there is an OTM 870 call option that is quoting at Rs.18. Let us also assume that this stock has 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? Let us look at the impact on the option price (using delta) and on the delta (using gamma).

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.

What happens to the delta? 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.

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 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 case of the 1 month option and the flattest for the 3 month option. That is because there is a 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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