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Jump diffusion model with application to the Japanese stock market

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  • Maekawa, Koichi
  • Lee, Sangyeol
  • Morimoto, Takayuki
  • Kawai, Ken-ichi

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Barndorff-Nielsen, N. Shephard, Econometrics of testing for jumps in financial economics using bipower variation, Unpublished discussion paper, Nuffield College, Oxford, 2004], which reveals that Japanese stock data has jumps.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

Suggested Citation

  • Maekawa, Koichi & Lee, Sangyeol & Morimoto, Takayuki & Kawai, Ken-ichi, 2008. "Jump diffusion model with application to the Japanese stock market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(2), pages 223-236.
    • Handle: RePEc:eee:matcom:v:78:y:2008:i:2:p:223-236
    DOI: 10.1016/j.matcom.2008.01.030
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    References listed on IDEAS

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    1. Sangyeol Lee & Jeongcheol Ha & Okyoung Na & Seongryong Na, 2003. "The Cusum Test for Parameter Change in Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 781-796, December.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
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    Cited by:

    1. Wang, Tiansong & Wang, Jun & Zhang, Junhuan & Fang, Wen, 2011. "Voter interacting systems applied to Chinese stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2492-2506.
    2. Xu, Weijun & Liu, Guifang & Li, Hongyi, 2016. "A novel jump diffusion model based on SGT distribution and its applications," Economic Modelling, Elsevier, vol. 59(C), pages 74-92.
    3. Yang Li & Yaolei Wang & Taitao Feng & Yifei Xin, 2021. "A New Simplified Weak Second-Order Scheme for Solving Stochastic Differential Equations with Jumps," Mathematics, MDPI, vol. 9(3), pages 1-14, January.
    4. Wajih Abbasi & Petr H jek & Diana Ismailova & Saira Yessimzhanova & Zouhaier Ben Khelifa & Kholnazar Amonov, 2016. "Kou Jump Diffusion Model: An Application to the Standard and Poor 500, Nasdaq 100 and Russell 2000 Index Options," International Journal of Economics and Financial Issues, Econjournals, vol. 6(4), pages 1918-1929.
    5. Tunaru, Radu & Zheng, Teng, 2017. "Parameter estimation risk in asset pricing and risk management: A Bayesian approach," International Review of Financial Analysis, Elsevier, vol. 53(C), pages 80-93.

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