Mastering Derivatives: Sensitivity of option strikes to volatility

Venkatesh Bangaruswamy | Updated on: Jun 03, 2022

An options trader should buy an option that will increase the most when volatility increases

Option price increases when volatility increases. As an options trader, you should buy an option that will increase the most when volatility increases. This week, we discuss the sensitivity of option strikes to changes in volatility.

Vega and implied volatility

If you are confident that an underlying is likely to move up, it is optimal to buy the underlying or its futures contract instead of buying call options. Why? Options lose value because of time decay which means a call option cannot move one to one with the underlying. In contrast, futures typically move in lockstep with the underlying. You can, therefore, capture larger gains when the underlying moves up.

In contrast, an increase in the underlying’s volatility means its prices fluctuate wildly. This uncertainty means buying the underlying or its futures contract is risky. Suppose the underlying declines by 100 points, the futures contract will lose nearly 100 points. That is when options are useful; the maximum loss is the option premium if the option expires out of the money (OTM). If there is still time for the contract to expire, losses will be lower because the option will carry some time value. The positive side is that you can gain some if the underlying moves up. This asymmetric payoff (higher gains, lower losses) makes options more valuable when volatility increases.

Note that the change in option price is different for in-the-money (ITM), at-the-money (ATM) and OTM options when volatility increases. So, it is important to observe an option’s vega to capture the sensitivity of an option price to changes in volatility. Vega is the change in the option value for a one percentage point change in volatility. Note that we use the actual option price instead of option value from a model. For instance, the vega of the next-week 16700 Nifty call is 10.99. With the current price at 185, an increase in implied volatility by one per cent could increase the option price to 196 (185 plus 10.99), all other factors remaining the same.

Basic fundas
Futures typically move in lockstep with the underlying
It’s possible to capture larger gains with ATM options
Increase in underlying’s volatility means its price fluctuates wildly

If you use a standard Black-Scholes-Merton option calculator and input variables from the NSE website, you will find that ATM option has the highest vega. For instance, with the Nifty Index trading at 16662, the next-week 16700 call is near-ATM with a delta of 0.49. This option’s vega of 10.99 is higher than the vega of 9.94 for the 16900 call. This suggests that ATM call could provide maximum absolute gains if volatility increases.

The change in option price can be approximately determined by multiplying the option vega with the expected change in volatility. For instance, if you expect implied volatility to jump by five percentage points, the approximate change in the ATM option’s price could be 54.95 points (5 times 10.99).

Optional reading

An ATM option’s gamma is typically large when implied volatility is low. It is the positive gamma that causes the option price to move up when volatility increases. With an ATM option having the highest gamma and vega, the increase in the option price is greater compared to OTM options for a given increase in volatility. If the higher volatility eventually translates into a price breakout, the ATM call could generate large gains as it will become ITM and gain intrinsic value. On the other hand, if the higher volatility leads to the same price change in the opposite direction, the ATM call will suffer lower losses; the positive gamma for long option reduces the magnitude of the call delta when the underlying declines.

The flipside to high gamma and vega is theta. If your forecast fails and volatility remains low, the ATM option will lose value because of passage of time. Note that the ATM option has the highest time value and, therefore, the highest theta. That is why betting on an ATM option is a trade-off between gamma and theta.

(The author offers training programmes for individuals to manage their personal investments)

Published on June 03, 2022
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