The Delta of a Variance Swap
Sébastien Bossu, Sebastian Gaitan-Escarpeta
Abstract
We define the variance swap delta as the sensitivity of the price of variance to a change in underlying price. We use Carr-Madan spanning formulas to analyze this sensitivity when the implied volatility smile curve may depend on the underlying price. We show that the variance swap total delta is zero for the class of smile curves that are pure functions of (log) moneyness, which goes against the empirical observation that variance is up when the market is down. We propose a simple modification of the smile to correct this issue.
Read the AI summary and key takeaways for traders on WOBR Quant Research.