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Explain how Gamma works in options — Kiran S. Prasad

Gamma is the most complicated among the option greeks. It does not measure the change in option premium. It is a measure that tracks the change in delta to changes in price of the underlying stock. As we have seen, delta measures the change in option premium in response to a change in price of the underlying stock. This delta, however, does not remain constant. It keeps changing.

For instance, consider the call option of Tata Steel with the strike price of Rs 390 expiring on August 26. On July 29, the price of the Tata Steel stock rose by Rs 15.10 to Rs 392.90. The premium for the 390 August call option rose by Rs 7. On July 30, however, when the stock price fell by nearly a rupee, the call option premium declined by close to 70 paise. The delta on July 30 had become larger compared to the delta on July 29. Gamma measures this change in delta.

Changes in delta are mainly related to the value of an option. When the underlying stock price is substantially above the strike price, then for every one-rupee change in the stock price, the option premium will change by an equivalent amount. That is delta will be close to one and will not change.

The Gamma then will also be low. Similarly, when an option is deep out of the money, changes in option premium will be small even for large changes in stock prices. The delta of the option will be close to zero. Then, too, the Gamma will be low.

Gamma will, however, tend to be high when the option is near the money. Consider the call option of Tata Steel. The moment the stock price rose above Rs 390, delta increased. In contrast, on July 29, Gamma of the option would have been higher and would have declined on July 30. And as the stock price rose to the levels of Rs 403 by August 6, the Gamma would have declined further.

Gamma is identical for both call and put options. Apart from the value of the option, Gamma also has a link with the time remaining to expiry of the option. The change in option premium in response to change in time to expiry is measured by the option greek, theta. Generally, as time to expiry increases, Gamma tends to rise, as does theta. The key difference is that Gamma is positive while Theta is negative.

Interplay of greeks

The interplay of delta, gamma and theta is important to determine the risks related to the option premium. The relevant factors to assess their interplay are:

*How far or near the option strike price is to the underlying stock price. Generally, the risks in the form of a change in option premium are higher if the strike price is near the price of the underlying.

*How much time remains until expiry. The risk of a fall in option premium is higher if the time to expiration is shorter

For instance, in the case of options near the money, Gamma is generally larger for an option that has a shorter time to expiration compared to an option that has a longer time to expiry. This indicates that as an option is near the money and the time is running out, changes in delta will be larger. Such an option will be subject to a changing delta, large gamma and large theta.

A grasp of the proportion of time value inherent in an option, the time remaining to expiration and the level of the shrike price relative to the underlying stock price can help us understand the risks even without looking at the numbers thrown up by the option greeks.

The understanding, however, would be relevant only if the options are priced properly. Options may not be priced properly, if the implied volatility built into option premium is substantially different from the recent trends in volatility of the stock price. Then changes in stock price may have only a marginal impact on the option premium. In such a case, the time value inherent in an option and understanding the effect of volatilities will assume prominence.

Queries relating to futures/options may be mailed to

fno@thehindu.co.in

or to Futures & Options, Kasturi & sons, 859-860, Anna Salai, Chennai 600 002.

Suresh Krishnamurthy

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