Pricing and Hedging Contingent Claims Using Variance and Higher-Order Moment Futures

Abstract

This paper suggests perfect hedging strategies of contingent claims under stochastic volatility and/or random jumps of the underlying asset price. This is done by enlarging the market with appropriate swap contracts whose payoffs depend on higher-order sample moments of the underlying asset price process. It also derives a model-free relation between these higher-order moment swaps and the value of a composite portfolio of European options, which can be employed to perfectly hedge variance swaps. Based on the theoretical results of the paper, and on options and variance swaps rates written on the S&P 500 index, the paper provides clear cut evidence that, first, random jumps are priced in the market and, second, hedging strategies for European options employing variance and higher-order moment swaps considerably improves upon the performance of traditional delta hedging strategies. These results indicate the kind of new financial instruments that can be introduced to perfectly hedge the market.