Pricing methods and hedging strategies for volatility derivatives

Abstract

We explore the valuation and hedging of discretely observed volatility derivatives using three different models for the price of the underlying asset: Geometric Brownian motion with constant volatility, a local volatility surface, and jump-diffusion. We begin by comparing the effects on valuation of variations in contract design, such as the differences between specifying log returns or actual returns and incorporating caps on the level of realized volatility. We then focus on the difficulties associated with hedging these products. Delta hedging strategies are ineffective for hedging volatility derivatives since they require very frequent rebalancing. Moreover, they provide limited protection in the jump-diffusion context. We study the performance of a hedging strategy for volatility swaps that establishes small, fixed positions in vanilla options at each volatility observation.