Last month in this column, we had discussed the sensitivity of option strikes to changes in volatility. Late last year, we had discussed how to create a synthetic long stock position using options. Stringing together both arguments, a reader wanted to know if a synthetic stock position will also be sensitive to changes in volatility. This week, responding to the reader’s question, we discuss characteristics of vega that explains why a synthetic stock will have near-zero vega exposure.

##### Vega factor

A synthetic stock can be set up by going long on an at-the-money (ATM) call and short on an ATM put. Note that vega is positive for long calls and long puts. Also, a call and a put on the same underlying with same expiration date and same strike must have the same vega, provided they have the same implied volatility.

To understand this argument, consider put-call parity. This equation, used for valuing puts, shows that two portfolios have the same payoff. One portfolio contains a put and an underlying stock that will be delivered if the put is exercised at expiry. The other portfolio has a same strike call and a bond. This bond matures at option expiry with maturity value equal to the amount needed to buy shares if the call is exercised at expiry.

As both portfolios have the same payoff, rearranging put-call parity, a long call and a short put must equal a long stock and short bond. That is, if you borrow money (short bond) to buy a stock, the payoff must match that of a long call and short put. Note that the long stock and short bond have zero vega, as they are not affected by implied volatility. Therefore, a long call and a short put ought to have zero vega, as their payoff is the same as that of the long stock and short bond.

If we move from the model world into real-world markets, the vega of a call may differ from that of a same strike put, albeit marginally. For instance, 17400 next-week Nifty call has a vega of 11.43 whereas the 17400 put has a vega of 11.42. Note that vega of 11.43 means that the call price will increase by 11.43 points for a one percentage point increase in implied volatility.

There are two other important characteristics of vega. The vega of an option tends towards zero as the option approaches expiration. Also, vega tends towards zero for options that are deep in-the-money (ITM) and deep out-of-the-money (OTM). For instance, the vega of the 18000 (deep OTM) next-week Nifty call is 4.29 and the 16800 call (deep ITM) is 4.64.

Vega basics
As time to expiration reduces and time value of an option declines, so does an option’s vega, assuming implied volatility remains the same

This discussion is relevant for your trading as it provides a perspective on what you should not do if you want your position to be vega-positive. That is, taking long positions in a stock, synthetic stock or futures is unlikely to generate gains when you expect volatility to increase. You must take long positions in ATM options or immediate OTM options to profit from volatility explosion.