Nonparametric Pricing and Hedging of Volatility Swaps in Stochastic Volatility Models

Abstract

In this paper the zero vanna implied volatility approximation for the price of freshly minted volatility swaps is generalised to seasoned volatility swaps. We also derive how volatility swaps can be hedged using a strip of vanilla options with weights that are directly related to trading intuition. Additionally, we derive first and second order hedges for volatility swaps using only variance swaps. As dynamically trading variance swaps is in general cheaper and operationally less cumbersome compared to dynamically rebalancing a continuous strip of options, our result makes the hedging of volatility swaps both practically feasible and robust. Within the class of stochastic volatility models our pricing and hedging results are model-independent and can be implemented at almost no computational cost.