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Working Paper

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

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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.
12.01.2006ISSN 2573-7953 WP 06-19DOI 10.26509/frbc-wp-200619
Keywords garch option models, stochastic volatility models with jumps, pricing and hedging options

Working Papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded official Federal Reserve Bank of Cleveland publications. The views expressed in this paper are those of the authors and do not represent the views of the Federal Reserve Bank of Cleveland or the Federal Reserve System.

Suggested Citation

Duan, Jin-Chuan, Peter Ritchken, and Zhiqiang Sun. 2006. “Jump Starting GARCH: Pricing and Hedging Options with Jumps in Returns and Volatilities.” Federal Reserve Bank of Cleveland, Working Paper No. 06-19. https://doi.org/10.26509/frbc-wp-200619