What is Gamma?
Option Greeks are the risk measures that are related to diverse roles in the trading of options. They help to analyze how different variables including prices, expiration date, and volatility impact the pricing of options. Many investors perceive these measures to be essential for making sound decisions in trading options.
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Gamma is a Greek alphabet used to find the change in the option price. It is the sensitivity of the change in the delta to the change in the underlying security, to understand gamma we need a good understanding of delta. Delta is the sensitivity of the change in the value of the option price to the change in the value of the underlying security.
Delta = change in the value of option/ change in the value of the underlying.
Delta explains the linear change in the option price due to change in underlying but delta capture only a small change in the option price to changes in the underlying. However, option prices are linear for a small change in the underlying but for a large change in the underlying the option prices are nonlinear and therefore we use gamma.
Gamma captures the curvature change in the value of the option price due to a change in the value of the underlying security It basically starts calculating options price where delta ends its calculation.
Gamma = Change in the delta/Change in the underlying security.
How it is Calculated?
Option gamma is the second derivation of the option price (value) function. We can express this using the following formula:
where,
d1 = [ln (S / K) + (r + ơ2/2) * t] / [ơ * √t]
q = Dividend yield of the asset
t = Time to the expiration of the option
So = Spot price of the underlying asset
ơ = Standard deviation of the underlying asset
K = Strike price of the underlying asset
r = Risk-free rate of return
Importance of gamma from the following perspective:
- ATM, ITM, and OTM option: Gamma is high for the ATM option, i.e. the difference between the underlying stock price and the strike price is zero. At this point, there is greater uncertainty of whether the option will be ITM or OTM at expiration. At this point, the option gamma is at the top of the bell curve in the below-mentioned picture.
- As the stock price increases or decreases the option will tend to move ITM or OTM. Gamma is the lowest for deep ITM or OTM options, which signifies that any change in the value of the underlying stock price has little or no impact on the option value.
- Maturity: Options with short term to expiration have higher option gamma then long-term options. In other words, short-term options are more sensitive. Option gamma increases as the option approach its maturity.
- Position in the option: Gamma is the same for a call option as well as for a put option. Gamma is negative for a short call and put and positive for a long call and put.
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- Delta: When gamma is high, option delta changes rapidly. When gamma is small, option delta changes relatively little.
- Forwards and Futures market: Gamma for a future and the forward contract is zero as the payoff of future and forward contract is linear and it measures only linear relation.
Author: Divya Sankhla
Divya has completed her graduation in Bachelors of Accounting and Finance. She has worked in Deloitte Touche Tohmatsu Services, Inc. as a Research Analyst for 1 year and at JM financial as a Credit Risk Analyst for 1.3 years. She is keen on learning about Financial Market. Well versed with Bloomberg, Capital Line, and Excel.
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