The Statistical Analysis of the Log-Return Series of the Chinese Stockprices: An Application of the Generalized Hyperbolic Distributions

中国股价日对数收益率的统计分析－广义双曲分布的应用

10.6338/JDA.200704_2(2).0008

李会琼(Hui-Qiong Li)；吴刘仓(Liu-Cang Wu)

广义的双曲分布 ； 厚尾 ； Kolmogorov-Smirnov检验 ； Generalized Hyperbolic Distribution ； Fat Tails ； Kolmogorov-Smirnov test

Journal of Data Analysis

2卷2期（2007 / 04 / 01）

161 - 178

英文

本文使用广义的双曲分布（GH分布），选取了深沪两市共11只股票，对股票价格的日对数收益率的概率分布进行了深入的研究。在所有的情形，GH分布都给出了非常令人满意的拟和。这表明GH分布作为股票日对数收益率的分布，在中国股市是一个很好选择。

This paper has studied the distributions of the log returns of the Chinese stock market, using the Generalized Hyperbolic Distributions (GH) as the reference distributions. The empirical results shows that in almost all the cases, both Normal Inverse Gaussian (NIG)distribution and the Hyperbolic distribution can fit the data very well.

1. (1996).Morgan Risk Technology Docoument.New York:Risk Metrics Group.
2. Esscher,F(1932),On the probability function in the collective theory of risk,Skandinavisk Aktuarietidskrift,15,175-195.
3. Andersen, T. G.,Bollerslev, T.,Diebold, F.,Labys, P.(2001).The Distribution of Realized Exchange Rate Volatility.Journal of Financial Economics,61,42-55.
4. Andersen, T. G.,Bollerslev, T.,Diebold, F.,Labys, P.(2001).The Distribution of Realized Exchange Rate Volatility.Journal of American Statistical Association,96,42-55.
5. Barndorff-Nielsen, O.(1977).Exponentially Decreasing Distributions for the Logarithm of Particle Size.Proceedings of the Royal Society London A,353,401-419.
6. Barndorff-Nielsen, O.(1997).Normal Inverse Gaussian distributions and Stochastic Volatitility Modelling.Sandn Journal of Statistics,24,1-13.
7. Barndorff-Nielsen, O.(1978).Hyperbolic Distributions om Hyperbolae.Sandn. Journal of Statistics,5,151-157.
8. Barndorff-Nielsen, O. E.(1998).Process of Normal Inverse Gaussian.Fiance and Stochastics,2,41-68.
9. Barndorff-Nielsen, O. E.,Blesild, P..Hyperbolic distributions and ramifications: Contributions to theory and application.Statistical Distributions in Scientific Work,Dordrecht:
10. Barndorff-Nielsen, O. E.,Jiang, Wenjiang.An initial analysis of German stock price series.Scand. J. Statist.
11. Black, F.,Scholes, M.(1973).The Pricing of Options and Corporate Liabilities.Journal of Political Economy,81(3),637-654.
12. Blasid, P.,Sorensen, M.(1992).Hyp a Computer Program for Analyzing Data by Means of the Hyperbolic Distribution.Department of Theoretical Statistics, Aarhus University.
13. Brigham, E. O.(1988).The fast Fourier Transform and Its Applications.New Jersey:Prentice Hall.
14. Eberlein, E.(2000).Mastering Risk.Prentice Hall.
15. Eberlein, E.,Keller, U.(1995).Hyperbolic Distributionsin Finance.Bernoulli,1995(1),281-299.
16. Fajardo, J.,Schuschnye, A.,Silva, A.(2001).Levy Processes and The Brazilian Market.Brazilan Review of Econometrics,21(2),263-289.
17. Gerber, H. U.,Shiu, E. S. W.(1994).Option pricing by Esscher transforms.Transactions of the Society of Actuaries,46,99-191.
18. Hanselmam. D. C.,Littlefield, B.(2001).Mastering Matlab 6-A Comprehensive Tutorial and Reference.Prentice Hall.
19. Hull, J.,White, A.(1987).The Pricing of Options on Asset with Stochastic Volatilities.Journal of Finance,52,281-300.
20. Jorion, P.(1997).Value at Risk: the New Benchmark for Controlling Market Risk.McGraw-Hill.
21. Keller, U.(1997).University of Freiburg.
22. Kupiec, P. H.(1995).Technique for Verifying the Accuracy of Risk Measurement Models.Journal of Derivatives,Winter,73-84.
23. Linden, M.(2001).A Model for Stock Returns Distribution.International Journal of Fiance Economics,6,159-169.
24. Nelder , J.,Mead, R.(1965).A Simplex Method for Function Minimization.Computer Journal,7,308-313.
25. Prause, K.(1999).University of Freiburg.
26. Raible, S.(2000).University of Freiburg.
27. Rydberg, Tian Hviid(2000).Realistic statistical modelling of financial data.International Statistical Review,68(3),233-258.
28. Ryderg, T.(1997).Why Financial Data are Interesting to Statisticians.Aarhus.