If you have a view that an underlying will rise 200 points, you will most likely buy an at-the-money (ATM) call or an immediate out-of-the-money (OTM) call. The question is whether it is optimal to buy an OTM strike that is equal to your price target for the underlying? This week, we discuss when such a bet will be gainful.

##### Time decay Vs Delta

The time value of an option becomes zero at expiry. Also, the ATM and the OTM options do not have intrinsic value. Therefore, both these options will have zero value at expiry. Suppose you buy an OTM option where the strike is equal to the price target. If the price target is achieved at expiry, the option will have zero value, causing losses on your long position equal to the option premium.

Assume the current price of an underlying is 700 and you expect the price to move to 800. You buy the 800 near-month call. If the strike intervals are in steps of 10, you are buying a deep OTM call. Your gains on the position come from delta, which is the change in the option price for a one-point change in the underlying. But a deep OTM option has a low delta. So, the gains are unlikely to be large. Therefore, your view should be that the underlying will reach your price target sooner than later; the sooner you sell the option, the greater the time value you will be able to recover. This means you must also have a view about the volatility of the underlying.

Suppose you buy the 18400 next-week Nifty call at 58 when the index is at 18070. If the index moves to 18200 in two days, the call price could be 76, an 18-point increase compared to the 130-point increase in the index. Note that the call delta is 0.24. That means the option should have moved by 31 points (0.24 times 130), but it did not. The reason is because in two days, the option lost value due to time decay. To understand the effect of time decay on the price, suppose the index reaches 18200 the day after you buy the call, its price could be 86 instead of 76.

Your gains would be even better if volatility explodes. For instance, if the Nifty Index reaches 18200 two days after you buy the 18400 call and the volatility jumps by two percentage points, the option value could be 94. This is because the position is long on vega, which is the sensitivity of the option to a one percentage-point change in implied volatility.

The point of this discussion is to suggest that the odds of winning are low if you buy a deep OTM option where the strike is equal to the target price. There is another factor. If you are trading based on price charts, it is relatively easy to forecast the direction of an underlying than the time when underlying could reach your price target. So, betting on a deep OTM strike may not be gainful.