Jump diffusion model with application to the Japanese stock market

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[O.E. Barndorff-Nielsen, N. Shephard, Econometrics of testing for jumps in financial economics using bipower variation, Unpublished discussion paper, Nuffield College, Oxford, 2004], which reveals that Japanese stock data has jumps.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.