A Guide to Volatility and Variance Swaps

Trading in derivatives has caused investors, and especially market makers, to be concerned with the volatility of asset returns along with their direction. Uncertain and time-varying volatility imparts risk to an otherwise hedged position, and volatility risk is not easy to manage with ordinary instruments. Volatility swaps are a new class of derivative, for which an asset9s volatility itself is the underlying. This article describes how volatility swaps work, and derives pricing and hedging equations for them. Interestingly, the natural derivative instrument in this family would be based on variance, rather than volatility, since a variance swap can be replicated (pretty well) by a static portfolio of ordinary European calls and puts on the price of the underlying asset. The authors also show how to set up a volatility hedge when the available traded options exhibit a smile or skew pattern.