Making an options book insensitive to volatility
Question
How can you combine vanilla calls and puts so that the resulting portfolio has zero vega?
Short answer
Offset vegas by holding options in the ratio of their vegas. For a long position in one option, sell units of another option with vega . The simplest example is long a call and short a put of the same strike and expiry: by put-call parity that is a forward, which has no vega at all. Vega neutrality is local, so the hedge must be rebalanced as spot, time and volatility move.
Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q2.47, p.20; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Greeks and Numerical Sensitivities
- Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
- Option Trading Strategies: Spreads, Combinations, and Payoff Engineering
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