Volatility is the most dominant of the five factors that are used as inputs to price an option. With most pricing models, you input the factors to find the value of an asset. With option pricing models, however, we find the volatility implied in the option price. This is because we do not use the model to find whether the option value is greater than the option price. Rather, we use the model to find which strike is cheaper. This week, we show that although historical volatility can be used to determine relative cheapness of options, it is simpler to apply the implied volatility rule.

##### Relative pricing

Suppose you want to buy the next week call on the Nifty Index, using the implied volatility rule, you will first select actively-traded strikes. Next, you will calculate the implied volatility of the strikes to determine which is cheaper.

What if you use historical volatility instead? Given that the next week options have nine days to expiry, you can determine the one-day volatility of the returns on the Nifty Index and then multiply this number by the square-root of nine. Suffice it to know that this calculation is based on the assumptions relating to volatility and the underlying’s returns distribution.

Now, suppose you determine that the historical volatility of the Nifty Index is 10 per cent. When you plug the historical volatility into the BSM model to determine the value of the 19700 and the 19800 next week calls, you will find that both strikes are overpriced. But the 19800 strike is less expensive, considering only time value. Therefore, you would choose that strike. Of course, you will arrive at that the same conclusion using the implied volatility rule, as you would pick the strike with the lowest implied volatility among the actively traded strikes.

The argument is simple. Time value of an option becomes zero at expiry. So, you want to choose the option that has the lowest time value among the actively-traded strikes, whether you apply historical or implied volatility. The point is that applying implied volatility is better for two reasons. One, implied volatility ignores the possibility that options can be overpriced or underpriced. If you believe that the underlying is likely to move up, you may want to buy an option because you are betting on gains from intrinsic value even if the option is overpriced. And two, calculating historical volatility is more time consuming than determining implied volatility.

Point to remember
Time value of an option becomes zero at expiry, and hence it is important to choose the option that has the lowest time value among the actively-traded strikes, whether you apply historical or implied volatility