Question

If an investor would like to buy a short-term straddle as he expects the volatility will jumps, what should be the sign (positive or negative) of gamma, vega, and theta for the strategy? Given the strategy is delta neutral.

Answer 1

A straddle is an options strategy which entails going long on a call and a put options of the same stock, at the same time, with the same strike price. The investor profits when the stocks moves quickly, one way or the other. He profits when the amount the stock moves is higher than the sum of the premium on both options.

Delta is the rate at which the price of an option will change if the stock moved by $1. Technically speaking, the straddle strategy is delta-neutral when it is at-the-money.

Gamma is the rate at which delta would change if the underlying stock moves $1.

If the underlying stock price rises or falls quickly, in other words if volatility increases, then the price of the straddle strategy would increase.

As the stock rises, the call rises in price more than the put falls in price. Similarly, as the underlying stock falls, the put rises in price more than the call falls. Either way, this creates a positive gamma. It means that the delta of the strategy moves in the same direction as the delta of the stock.

Option theta stands for time decay. Since a straddle consists of two long positions, the price of the straddle falls as it gets closer to expiration date. Hence the straddle has a negative theta.

Finally, Vega is the rate at which the price of an option or strategy changes given a corresponding one-point change in the implied volatility of the stock. The straddle strategy performs well when there is volatility in the stock. Hence the price of a straddle increases when volatility increases and falls when volatility falls. Hence a straddle is positive Vega.