Statistical properties of the volatility in the Korea composite stock price index

Journal of the Korean Physical Society

Volumn 47, Issue 6, 2005, Pages 1059-1063

  Lee, Chang Yong ^a   Ree, Suhan ^a  

^a Kongju National University   (South Korea)

Author keywords

Correlation; KOSPI; Stock; Volatility

Indexed keywords

EID: 30344488430     PISSN: 03744884     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. D. Challet and Y-C. Zhang, Physica A 246, 407 (1997).
2. R. Mantegna and E. Stanley, An Introduction to Econophysics (Cambridge University Press, Cambridge, 2000), Chap. 4.
3. L. Bachelier, Ann. Sci. Ecole Norm. Sup. 3, 21 (1900).
4. R. Mantegna and H. E. Stanley, Nature 376, 46 (1995).
5. Y. Liu, P. Gopikrishnan, P. Cizeau, M. Meyer, C-K. Peng and H. E. Stanley, Phys. Rev. E 60, 1390 (1999), and references therein.
6. K. Lee and J. Lee, J. Korean Phys. Soc. 44, 668 (2004).
7. H-J. Kim, I-M. Kim, Y. Lee and B. Kahng, J. Korean Phys. Soc. 40, 1105 (2002).
8. Y. Nakajima, J. Korean Phys. Soc. 40, 1096 (2002).
9. A. Górski, S. Drodz and J. Septh, Physica A 316, 496 (2002).
10. S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner and Y. Dodge, Nature 381, 767 (1996).
11. K. Matia, Y. Ashkenazy and H. Eugene Stanley, Europhy. Lett. 61, 422 (2003).
12. The volatility in terms of the price change in the logarithm of the S&P500 index has been studied in Ref. 5. The authors of Ref. 5 showed that the volatility distribution followed a lognormal with a power-law asymptotic behavior and that the volatility had a long-range correlation.
13. Another way to define the price change is the difference in the logarithm of the price, that is, G(t) = In Z(t + ∇t) - In Z(t). The main reason for this definition is to compensate for a logarithmically increasing global trend that a stock index may have. Such a trend can be found, for instance, in the S&P500 [5]. In the case of the KOSPI, however, there is no such trend, as can be seen in Fig. 1 (a); thus, we adopt Eq. (1) as the definition of the price change.
14. Various methods for detecting a long-range dependence can be found: for example, in Jan Beran, Statistics for Long-Memory Processes (Chapman & Hall/CRC, 1994), p. 41.
15. A. Pagan, J. Empirical Finance 3, 15 (1996).
16. F. Black and M. Scholes, J. Polit. Econ, 81, 637 (1973).
17. J. Cox, S. Ross and M. Rubinstein, J. Financial Econ. 7, 229 (1979).
18. A random variable X is log-normally distributed when Y = In X is normally distributed. Thus, if a random variable X follows a log-normal distribution, then Z = (In X - μ)/σ is a random variable of the standard Gaussian distribution N(0,1).
19. B. Silverman, Density Estimation for Statistics and Data Analysis (Chapman & Hall/CRC, 1986), p. 34.
20. C-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley and A. L. Goldberger, Phys. Rev. E 49, 1685 (1994).
21. C-K. Peng, S. Havlin, H. E. Stanley and A. Goldberger, Chaos 5, 82 (1995).
22. In DFA, a local trend is usually represented by fitting a linear equation using a linear least-squares fit. Any non-linear regression, however, can also be used.
23. R. Engle, Econometrica 50, 987 (1982).
24. T. Bollerslev, J. Econometrics 31, 307 (1986).