# Mastering derivatives: characteristics of the vega option

Last month in this column we discussed the sensitivity of option strikes to changes in volatility. At the end of last year, we discussed how to create a synthetic long position in stocks using options. Linking the two arguments, one reader wanted to know if a position in synthetic stocks would also be sensitive to changes in volatility. This week, in response to the reader’s question, we discuss the characteristics of vega that explain why a synthetic stock will have near-zero vega exposure.

Vega Factor

A synthetic stock can be created by taking a long position on an ATM call and a short position on an ATM put option. Note that vega is positive for long calls and long puts. Moreover, a call and a put on the same underlying with the same expiration date and the same strike price must have the same vega, provided they have the same implied volatility.

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

Since both portfolios have the same gain, rearranging the put-call parity, a long call and a short put should equal one long stock and one short bond. That is, if you borrow money (short bond) to buy a stock, the gain should equal that of a long call and a short sell. Note that long stocks and short bonds have zero vega, as they are unaffected by implied volatility. Therefore, a long call and a short put should have zero vega because their payoff is the same as the long stock and the short bond.

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

There are two other important features of vega. An option’s vega tends to zero as the option nears expiration. Also, vega tends to zero for deep-in-the-money (ITM) and deep-out-of-the-money (OTM) options. For example, next week’s Nifty 18000 (deep OTM) call vega is 4.29 and the 16800 (deep ITM) call is 4.64.

The basics of Vega

As the time to expiration decreases and the time value of an option decreases, the vega of an option also decreases, assuming the implied volatility remains the same

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

Optional reading

The observation that vega tends to zero as the option nears expiration relates to the relationship between time value and implied volatility. As the time to expiration decreases and the time value of an option decreases, the vega of an option also decreases, assuming the implied volatility remains the same. If the implied volatility decreases, the vega of an option decreases according to the time value. This understanding of vega is helpful when shorting options because time decay works in your favor.

You need to be careful with long option positions because the decay over time will accelerate when the implied volatility decreases.

Conversely, long vega positions are valuable when you expect implied volatility to explode. The flip side is that options that have a large vega could also have a large time value, exposing the position to a large time decay.

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

Published on

August 06, 2022