Jump Starting GARCH: Pricing and Hedging Options With Jumps in Returns and Volatilities

Abstract

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Our model nests Duan's GARCH option models, where conditional returns are constrained to being normal, as well as mixed jump processes as used in Merton. The diffusion limits of our model have been shown to include jump diffusion models, stochastic volatility models and models with both jumps and diffusive elements in both returns and volatilities. Empirical analysis on the S&P 500 index reveals that the incorporation of jumps in returns and volatilities adds significantly to the description of the time series process and improves option pricing performance. In addition, we provide the first-ever hedging effectiveness tests of GARCH option models.

Keywords: GARCH option models, stochastic volatility models with jumps, pricing and hedging options