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

45 Pages Posted: 14 Dec 2003 Last revised: 30 Oct 2007

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

Date Written: December 2006

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

Suggested Citation

Duan, Jin-Chuan and Ritchken, Peter H. and Sun, Zhiqiang, Jump Starting GARCH: Pricing and Hedging Options With Jumps in Returns and Volatilities (December 2006). FRB of Cleveland Working Paper No. 06-19; AFA 2004 San Diego Meetings. Available at SSRN: https://ssrn.com/abstract=479483 or http://dx.doi.org/10.2139/ssrn.479483

Jin-Chuan Duan

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

1 Business Link
Singapore, 117592
Singapore

Peter H. Ritchken (Contact Author)

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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