Question

The FTSE index is at 5,100. A firm is short a straddle on the FTSE 100 struck at 5,100 and long a 5,000/5,200 strangle. If volatility were to increase,

a) The value of their position would increase.

b)The value of their position would be unaffected.

c) The value of their position would decrease.

d) any of the above is possible.

Answer 1

Theoretically, if volatility increases, the value of the given position would decrease slightly as the increase in volatility will lead to an increase in prices of all options of both the straddle & strangle. The loss in short straddle will be largely completely compensated by an increase in the value of strangles, leaving just a minor loss in the position. You can verify this using any option calculator or Black-Scholes formula.

But practically, when volatility increases, its effect is different across different strike prices. That is why we see different implied volatilities (IVs) for different strike prices in the option quotes provided by the exchanges. The implied volatility is usually higher for Out of the Money (OTM) options (which are used for creating a strangle). This concept is also sometimes called as volatility smile due to the smile shaped graph of implied volatility vs strike prices.

So, the exact effect of the given situation cannot be predicted and thus the correct option would be d) any of the above is possible.