Approximating Garch-Jump Models, Jump-Diffusion Processes, and Option Pricing

32 Pages Posted: 21 Jun 2006

See all articles by Jin-Chuan Duan

Jin-Chuan Duan

National University of Singapore (NUS) - Business School and Risk Management Institute

Peter H. Ritchken

Case Western Reserve University - Department of Banking & Finance

Zhiqiang Sun

National City Bank

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.

Suggested Citation

Duan, Jin-Chuan and Ritchken, Peter H. and Sun, Zhiqiang, Approximating Garch-Jump Models, Jump-Diffusion Processes, and Option Pricing. Mathematical Finance, Vol. 16, No. 1, pp. 21-52, January 2006. Available at SSRN: https://ssrn.com/abstract=910639 or http://dx.doi.org/10.1111/j.1467-9965.2006.00259.x

Jin-Chuan Duan (Contact Author)

National University of Singapore (NUS) - Business School and Risk Management Institute ( email )

1 Business Link
Singapore, 117592
Singapore

Peter H. Ritchken

Case Western Reserve University - Department of Banking & Finance ( email )

10900 Euclid Ave.
Cleveland, OH 44106-7235
United States
216-368-3849 (Phone)
216-368-4776 (Fax)

Zhiqiang Sun

National City Bank ( email )

National City Center
1900 East Ninth Street
Cleveland, OH 44114-3484
United States

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