This article provides comprehensive tests of alternative jump-diffusion models for the purpose of hedging S&P 500 options. We explicitly take into account the risk arising from price and variance jumps and assess the hedging performance by focusing on the ability of competing specifications to forecast hedging errors. To this end, we devise density prediction tests and find evidence that jumps are important features of S&P 500 index dynamics. All jump-diffusion models tested in this article show signs of misspecification, but the inclusion of jumps can improve the hedging performance and risk assessment, especially in two-instrument hedges.

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