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APPROXIMATING GARCH-JUMP MODELS, JUMP-DIFFUSION PROCESSES, AND OPTION PRICING

Authors


  • This paper benefits from the comments by the two anonymous reviewers and the participants of the 2004 American Finance Association meetings in San Diego, the Daiwa International Workshop in Financial Engineering held in Tokyo and Kyoto in August 2004, the 2004 Annual Derivatives Conference in New York, the Conference on Financial and Economic Policies and Financial Engineering in Taipei in May 2004, the Workshop on Mathematical Finance and Insurance in Huangshan, China in May 2004 and the Risk Management in Insurance Conference at University of Waterloo in June 2004. The authors also thank the seminar participants at Providence University and the National Center for Theoretical Sciences in Taiwan for their comments. Financial support from both the Social Sciences and Humanities Research Council of Canada and the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.

Address correspondence to Jin-Chuan Duan Rotman School of Management, University of Toronto, Ontario, Canada M5S 3E6; e-mail: jcduan@rotman.utoronto.ca.

Abstract

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset prices and volatilities. We extend theory developed by Nelson (1990) and Duan (1997) by considering the limiting models for our approximating GARCH Jump process. Limiting cases of our processes consist of models where both asset price and local volatility follow jump diffusion processes with correlated jump sizes. Convergence of a few GARCH models to their continuous time limits is evaluated and the benefits of the models explored.

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