This paper was previously circulated under the title “Asset Pricing under Jump Diffusion” (Zhang and Zhao 2006). We are especially grateful to an anonymous referee for valuable comments and suggestions. We also acknowledge helpful comments from Andrew Carverhill, Min Dai, Jin-Chuan Duan, Nengjiu Ju, Jun Liu (our CICF discussant), Chenghu Ma, Dilip Madan (managing editor), Rujing Meng, Jun Pan, Yanmin Qian, Duo Wang, Keith Wong, Junxi Zhang, Xiaoqian Zhang, Yingzi Zhu, and seminar participants at the University of Hong Kong (HKU), Shanghai Jiao Tong University, Zhejiang University, Central University of Finance and Economics, Tsinghua University, Peking University, National University of Singapore, Quantitative Methods in Finance Conference (QMF) 2006 in Sydney, Asian Finance Association/Financial Management Association Annual Meeting 2007 in Hong Kong, and 2007 China International Conference in Finance (CICF 2007) in Chengdu. Jin E. Zhang has benefited from interesting discussions with Stephen Ching, Stephen Chiu, Nan Li, Tiecheng Li, Tao Lin, Stephen Ross, C.Y. Tse, Oldrich Vasicek, Jiang Wang, and Hong Yan. The research of this paper was partially supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7403/06H, HKU 7179/07E and HKU 7549/09H).
EQUILIBRIUM ASSET AND OPTION PRICING UNDER JUMP DIFFUSION
Article first published online: 5 DEC 2010
© 2010 Wiley Periodicals, Inc.
Volume 22, Issue 3, pages 538–568, July 2012
How to Cite
Zhang, . J. E., Zhao, H. and Chang, E. C. (2012), EQUILIBRIUM ASSET AND OPTION PRICING UNDER JUMP DIFFUSION. Mathematical Finance, 22: 538–568. doi: 10.1111/j.1467-9965.2010.00468.x
- Issue published online: 6 JUN 2012
- Article first published online: 5 DEC 2010
- Manuscript received June 2009; final revision received May 2010.
- asset pricing;
- option pricing;
- jump diffusion;
- equity risk premium;
- variance risk premium
This paper develops an equilibrium asset and option pricing model in a production economy under jump diffusion. The model provides analytical formulas for an equity premium and a more general pricing kernel that links the physical and risk-neutral densities. The model explains the two empirical phenomena of the negative variance risk premium and implied volatility smirk if market crashes are expected. Model estimation with the S&P 500 index from 1985 to 2005 shows that jump size is indeed negative and the risk aversion coefficient has a reasonable value when taking the jump into account.