# Mastering Derivatives: Betting on volatility – BusinessLine Exchange-traded options are not a pure bet on volatility. Other factors such as spot price, strike price, time to maturity and interest rate also drive option prices. Yet, you can trade options to profit from mispriced volatility. In this article, we discuss how to setup one such strategy- long underlying and short at-the-money (ATM) option on the underlying.

Realized Vols Vs Implied Vols

Volatility that is implied in the option price based on a model (Black-Scholes-Merton model, for instance) is referred to as implied volatility. So, if the implied volatility extracted from an option price is 10 per cent and the option has 15 days to expiry, an inference is that the market expects the volatility of the underlying to be 10 per cent over the next 15 days. Realized volatility is the actual volatility of the underlying that occurs during the remaining life of the option (15 days in this instance).

Implied volatility does not correctly forecast realized volatility because option price is also exposed to changes in volatility. That is, implied volatility should be different from realized volatility because of the risk associated with changing volatility. Empirical evidence suggests that implied volatility is typically higher than realized volatility. This means shorting ATM options should be profitable. Why?

Implied volatility is part of time value of the option; the other component is time to maturity. The time value of an option must become zero at expiry. This is because the option becomes less valuable with each passing day. The loss in time value is accelerated when implied volatility declines. And implied volatility could decline when the market adjusts down expected volatility as the option approaches expiry.

If you have a view that realized volatility is likely to be lower than implied volatility, you can setup a strategy that is long the underlying and short the ATM option on the underlying. Suppose you setup this strategy on Reliance Industries. With the stock currently trading at 2320, you should short the 2320 call option which is currently at 57. The delta of the call is 0.52. Given that the permitted lot size of the contract is 250, you should buy 130 shares of the stock. That is, the number of shares you buy must be determined by multiplying the permitted lot size by the call option delta.

So, what happens to the strategy if the stock trades at, say, 2380 six days before expiry? Even if you assume that the implied volatility is the same, the option could be worth 72 points. That means you lose 15 points (72 less 57) on the short call for a total loss of 3750 per contract. But your long stock would carry 60-point gain (2380 less 2320) for a total of 7800. Therefore, the strategy could fetch a net gain of 4050 (7800 less 3750). This gain will be greater if the implied volatility declines. Note that the strategy will suffer losses if the stock moves faster because the loss on the short calls will be more than the gains on the long stock position.