There is something unique about the Greek option, gamma. This week, we discuss the characteristics of gamma including its relation to volatility and time.
Advantage long positions
Unlike delta which benefits a long position when an underlying moves in the desired direction and causes harm when the underlying moves in the opposite direction, gamma helps long positions whether an underlying moves up or down. How?
Traders experience increasing gains from long calls when an underlying moves up and decreasing losses when the underlying declines. Likewise, traders experience increasing gains from long puts when an underlying declines and decreasing losses when the underlying rises.
The near-week 18700 Nifty call has a gamma of 0.0015.
So, if the Nifty Index were to increase by one point, the delta of the 18700 call is likely to increase by 0.0015 point. Likewise, if the Nifty Index were to decrease by one point, the delta of the 18700 call is likely to decline by 0.0015 point. Note that delta captures the increase or decrease in option value when the underlying moves up or down. And gamma accelerates the call delta on the upside and decelerates the delta on the downside. Therefore, gamma is added to delta to arrive at a new delta when the underlying moves up and is deducted from delta to arrive at a new delta when the underlying declines.
We know that an increase in the volatility of an underlying increases an option price. It is gamma that drives an option’s sensitivity to volatility. Note that vega captures the sensitivity of an option price to change in volatility. An option that has a small gamma will also have a small vega. Deep in-the-money (ITM) options have low vega and low gamma. At-the-money (ATM) call and put have the highest vega and the highest gamma.
Finally, gamma is the primary reason why an option price has time value. That is, an option’s time value is the result of asymmetric payoffs — large upside potential with limited downside risk. Referred to as the theta-gamma trade-off, an option that has the largest gamma will also have the largest theta. Thus, when an underlying experiences small price movements and volatility is expected to remain low, the option on the underlying will decline in value with passage of time.
Positive gamma is a desirable factor for long positions. What is good for long positions is bad for short positions. Because of their negative gamma exposure, short positions tend to experience smaller gains and larger losses for a given change in the underlying. Despite this, professional traders take short positions because options often expire worthless. But be mindful that short positions experience small frequent gains and large infrequent losses. A final note: Gamma tends to move towards zero the farther the strikes are from ATM. This observation makes sense when you consider that an option’s delta tends towards zero for deep ITM and OTM options.
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