Previously in this column, we discussed how to choose between an out-of-the-money (OTM) call and OTM put that are equidistant from an underlying. But what if you have identified a strike and want to decide whether to short a call or a put? This week, we discuss why same strike call and put will likely have same vega and gamma, and yet offer different profit potential for short positions.

Gamma and vega

Consider the next-week 17700 Nifty call and put. With the index currently at 17624, the call is OTM whereas the put is in-the-money (ITM). The vega of the 17700 call is nearly equal to the 17700 put and so is the gamma. Vega captures the change in option price for a one percentage-point change in implied volatility, whereas gamma captures the change in delta for a one-point change in the underlying. Note that both vega and gamma are positive for calls and puts.

There is some conceptual support to why same strike, same expiry call and put should have the same vega and gamma. Consider two portfolios. One portfolio carries a long call and a long bond equal to the present value of the strike. The other portfolio carries a long put and the underlying stock. Note that a long stock has zero vega and gamma. Based on put-call parity, both portfolios must be equal. Rearranging the positions in the portfolios, a long stock must be equal to a long call, the long bond, and a short put. Now, this combination must also have zero vega and gamma, as it is a synthetic stock position. That means the positive gamma and vega from long call must be cancelled by the negative gamma and vega from the short put. That is possible only if both the call and the put have the same gamma and vega.

Take note
When the underlying declines, short put offers lower gains than the short call

But the profit potential from both strikes may not be the same for a given change in the underlying. Suppose the Nifty Index were to decline to 17600 four days later. The call will likely decline 38 points compared with a five-point decline in the put. If the Nifty Index were to instead increase to 17650 four days later, the call will likely decline by 19 points and the put by 35 points. Why?

The initial delta is different for both strikes. Therefore, when the underlying moves up to 17650, for instance, the call delta increases marginally whereas put delta decreases. This leads to the short call offering lower gains than the short put. Likewise, when the underlying declines, short put offers lower gains than the short call.

Optional reading

Even if the index were to remain at the same level four days after you buy the call or the put, the profit potential is likely to be different because of the difference in time decay between the options. Delta and time decay, therefore, account for the difference in profit potential.

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

Related Topics