Question

Question
Can the vega of a derivative portfolio be changed by taking a position in the underlying asset? Explain your answer

Answer 1

The Vega of an option 'v' is the rate of change in its value with respect to the volatility of the underlying asset.

A position in the underlying asset has zero Vega. Therefore , Vega cannot be changed by taking a position in the underlying asset. In this respect, vega is like gamma . A complication is that different options a portfolio are liable to have different implied volatilites. If all implied volatilities are assumed to change by the same amount during any short period of time, Vega can be treated like gamma and the Vega risk in a portfolio of options can be hedged by taking a position in the single option. lf 'V' is the Vega of a portfolio and Vr is the Vega of a traded option , a position of -V/Vr in the traded option makes the portfolio instantaneously Vega neutral.Unfortunately , a Portfolio that is gamma neutral will not in general be Vega neutral and vice versa .If a hedger requires a portfolio to be both gamma neutral and Vega neutral, at least two of the traded options dependent on the underlying assets must be used.