Power tails of index distributions in chinese stock market

Physica A: Statistical Mechanics and its Applications

Volumn 377, Issue 1, 2007, Pages 166-172

  Zhang, J W ^a,b,c   Zhang, Y ^a   Kleinert, H ^c  

^a SHIHEZI UNIVERSITY   (China)

^b PEKING UNIVERSITY   (China)

^c FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

L vy distribution; Power law; Stock market index

Indexed keywords

DATA REDUCTION; STATISTICAL METHODS;

POWER-LAW DISTRIBUTION; STOCK MARKET INDEX;

INVENTORY CONTROL;

EID: 33846237801     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2006.11.012     Document Type: Article

References (52)

1. Bachelier L. Ann. Sci. École Norm. Suppl. 3 (1900) 21
2. Kendall M.J. J. Roy. Stat. Soc. 96 (1953) 11
3. Roberts H.V. J. Finance 14 (1959) 1
4. Osborne M.M. Oper. Res. 7 (1959) 145
5. Mandelbrot B.B. J. Business 36 (1963) 294
6. Mandelbrot B.B. Fractals and Scaling in Finance (1997), Springer, Berlin
7. J.P. Bouchaud, M. Potters, Theory of Financial Risks: From Statistical Physics to Risk Management, Cambridge University Press, Cambridge, 2000, 2003, The first and the second extension editions.
8. I. Kondor, J. Kértesz, (Eds.), Econophysics: An Emerging Science, Kluwer, Dordrecht, 1999.
9. Mantegna R.N., and Stanley H.E. An Introduction to Econophysics: Correlations and Complexity in Finance (1999), Cambridge University Press, Cambridge
10. R.N. Mantegna, (Ed.), Proceedings of the International Workshop on Econophysics and Statistical Finance, Physica A 269 (1999), Special issue.
11. Sornette D. Why Stock Markets Crash: Critical Events in Complex Financial Systems (2003), Princeton University Press, Princeton
12. H. Kleinert, Path integrals in quantum mechanics, statistics, polymer physics, and financial markets, World Scientific, Singapore, 2004, third extended edition. 〈http://www.physik.fu-berlin.de/∼kleinert/b5〉.
13. Zhang J.W., and Wang C.S. A Glimpse of Econophysics. In: Zhao K.H., and Qin K.C. (Eds). Physics Lightens the World (2005), Peking University Press, Beijing
14. Dacorogna M.M., Zuller U.A.M., Nagler R.J., Oslen R.B., and Pictet O.V. J. Int. Money Finance 12 (1993) 413
15. Mantegna R.N., and Stanley H.E. Nature 376 (1995) 46
16. B. Grigelionis, Lith. Math. J. 39 (1999) 33. See also www.maf.vu.lt/mif/mokslas/MAF00pre.html for a technical report of the author;
17. W. Schoutens, Meixner Processes in Finance, Report 2001-002, EURANDOM, Eindhoven. (www.eurandom.tue.nl/reports/2001/002wsreport.ps).
18. Fouqué J.P., Papanicolaou G., and Sircar K.R. Derivatives in Financial Markets with Stochastic Volatility (2000), Cambridge University Press, Cambridge
19. Fouqué J.P., Papanicolaou G., and Sircar K.R. Int. J. Theor. Appl. Finance 3 (2000) 101
20. Stanley M.H.R., Nunes Amaral L.A., Buldyrev S.V., Havlin S., Leschhorn H., Maass P., Salinger M.A., and Stanley H.E. Nature 379 (1996) 804
21. Sornette D., Johansen A., and Bouchaud J.P. J. Phys. I (France) 6 (1996) 167
22. Plerou V., Nunes Amaral L.A., Gopikrishnan P., Meyer M., and Stanley H.E. Nature 400 (1999) 433
23. Plerou V., Gopikrishnan P., Rosenow B., Nunes Amaral L.A., and Stanley H.E. Phys. Rev. Lett. 83 (1999) 1471
24. The price fluctuations are usually described by the variable "return", which is defined as the forward change in the logarithm of price. Some studies use the difference in the price instead, such as in Refs. [15,36]. However, both have the same statistics for events that are not too large [25].
25. Lux T. Appl. Fin. Econ. 6 (1996) 463
26. Gopikrishnan P., Meyer M., Nunes Amaral L.A., and Stanley H.E. Eur. Phys. J. B 3 (1998) 139
27. Gopikrishnan P., Plerou V., Nunes Amaral L.A., Meyer M., and Stanley H.E. Phys. Rev. E 60 (1999) 5305
28. Plerou V., Gopikrishnan P., Nunes Amaral L.A., Meyer M., and Stanley H.E. Phys. Rev. E 60 (1999) 6519
29. Wang B.H., and Hui P.M. Eur. Phys. J. B 20 (2001) 573
30. x ≃ 16 days for returns of stock prices of US individual companies [26].
31. An empirical study (Ref. [32]) suggests that stock prices are in a different universality class other than spot prices for commodities.
32. Gopikrishnan P., Plerou V., Gabaix X., and Stanley H.E. Phys. Rev. E 62 (2000) R4493
33. Plerou V., Gopikrishnan P., Nunes Amaral L.A., Gabaix X., and Stanley H.E. Phys. Rev. E 62 (2000) R3023
34. Matia K., Nunes Amaral L.A., Goodwin S.P., and Stanley H.E. Phys. Rev. E 66 (2002) 045103R
35. Solomon S., and Richmond P. Physica A 299 (2001) 188
36. Gabaix X., Gopikrishnan P., Plerou V., and Stanley H.E. Nature 423 (2003) 267
37. Daniels M.G., Farmer J.D., Gillemot L., Iori G., and Smith E. Phys. Rev. Lett. 90 (2003) 108102
38. Huang Z.F. Physica A 287 (2000) 405
39. Tang L.H., and Huang Z.F. Physica A 288 (2000) 444
40. K. Matia, M. Pal, H.E. Stanley, H. Salunkay, cond-mat/0308013.
41. Cajueiro D.O., Tabak B.M., and Souza N.A. Physica A 351 (2005) 512
42. On the American market, these are usually referred as overnight returns.
43. The Shanghai Stock Exchange (SSE) is the first market of government-approved securities which was founded in Shanghai on November 26, 1990 and started operating on December 19 of the same year. The SSE index is usually considered as a benchmark of the Chinese equity performance.
44. The data are provided by the Stock Star Corporation, 〈http://www.stockstar.com〉.
45. The values of α are sensitive to the bounds of the region used for fitting [25]. The error caused by the missing digits that might affect the values of α has been checked and removed [26].
46. Yan C., Zhang J.W., Zhang Y., and Tang Y.N. Physica A 353 (2005) 425
47. Y. Zhang, M.Sc. Thesis, Peking University, 2005.
48. Hill B.M. Ann. Stat. 3 (1975) 1163
49. Hall P., and Welsh A.H. Ann. Stat. 13 (1985) 331
50. Phillips P.C.B. J. Appl. Econ. 11 (1996) 1
51. There are two time periods within a trading day in Chinese stock market. The morning session runs from 9:30 to 11:30, and the afternoon session runs from 13:00 to 15:00. Therefore, the length of a trading day is 242 minutes.
52. i) are removed, the distribution of returns retains its power-law form. The tail exponents (α ≃ 3.52 for the positive tail and α ≃ 4.34 for the negative tail) are only a little larger than those caused by the overnight returns.