Quadratic hedging strategies for volatility swaps

This paper investigates a variance-optimal hedging strategy for volatility swaps under exponential Lévy dynamics. To obtain the optimal initial capital and the optimal amount of the underlying asset, we derive the explicit expressions of the Föllmer-Schweizer decomposition, which in turn implies the explicit expressions of hedging strategies. Numerical results are presented to show the performances of variance-optimal hedging strategies through comparing with other hedging methods.