Jump diffusion model with application to the Japanese stock market

Authors:
Koichi Maekawa;Sangyeol Lee;Takayuki Morimoto;Ken-ichi Kawai
Affiliations:
Department of Economics, Hiroshima University of Economics, Hiroshima, Japan;Department of Statistics, Seoul National University, Seoul, South Korea;Department of Graduate School of Economics, Hitotsubashi University, Tokyo, Japan;Risk Analysis Research Center, The Institute of Statistical Mathematics, Tokyo, Japan
Venue:
Mathematics and Computers in Simulation
Year:
2008

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Abstract

In this paper we demonstrate that a jump diffusion model is better fitted to Japanese stock data in the Nikkei 225 than the classical Black-Scholes (BS) model. In order to check the existence of jumps, we implement the bipower test by Barndorff-Nielsen and Shephard [O.E. Barndorff-Nielsen, N. Shephard, Econometrics of testing for jumps in financial economics using bipower variation, Unpublished discussion paper, Nuffield College, Oxford, 2004], which reveals that Japanese stock data has jumps. For modeling the data, we choose Kou's [S.G. Kou, A jump diffusion model for option pricing, Manage. Sci. 48 (2002) 1086-1101] model for its tractability and rich theoretical implications. We compare the option prices obtained from Kou's and BS' models with real market prices. The comparison study confirms that Kou's model outperforms the BS model.