YOUR KILLER EQUITIES INTERVIEW QUESTIONS: How does the delta and gamma evolve through time on a variance swap...
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THE QUESTION: How does the delta and gamma evolve through time on a variance swap, if a long position is hedged with options and the stock moves up what is your hedge to retain delta neutrality?
THE SUGGESTED ANSWER
Sure if you have ever traded them or studied the Maths, these are easy questions, but the vast majority of people in equities haven't. The delta does exist, but it is effectively zero as it resets everyday since there is no moneyness in a variance swap.
The gamma is constant throughout the life of the instrument unless the convexity changes.
Although it wasn't asked (but could have been), the vega declines linearly over time. As for the second part of the question, if there is no delta on your var swap and you have sold options to hedge the long var swap position, you have negative gamma on that position, which will result on you needing to buy stock in an up move to remain delta neutral overall.