A Note on Variance Swap Greeks

This note provides closed-form expressions for spatial Greeks (Delta and Gamma) for discretely monitored realized variance swaps under several common parametric model assumptions. We derive closed-form results for stochastic volatility and exponential L´evy models, as well as some approximations in the case of stochastic local volatility. We show that variance swap Greeks are inherently sensitive to model assumptions, and the common practice of ignoring the variance swap delta is not always appropriate. In particular, the Delta of a variance swap under a stochastic local volatility model can be quite significant under certain conditions, engendered by the local volatility skew, especially when the contract is close to inception and has many remaining observations