Summary
This paper investigates the statistical properties of absolute log-returns, defined as the absolute value of the logarithmic price change, for the Nikkei 225 index in the 28-year period from January 4, 1975 to December 30, 2002. We divided the time series of the Nikkei 225 index into two periods, an inflationary period and a deflationary period. We have previously [18] found that the distribution of absolute log-returns can be approximated by the power-law distribution in the inflationary period, while the distribution of absolute log-returns is well described by the exponential distribution in the deflationary period.
To explain these empirical findings, we have introduced a model of stock market dynamics [19,20]. In this model, the stock market is composed of two groups of traders: the fundamentalists, who believe that the asset price will return to the fundamental price, and the interacting traders, who can be noise traders. We show through numerical simulation of the model that when the number of interacting traders is greater than the number of fundamentalists, the power-law distribution of absolute log-returns emerges from the interacting traders' herd behavior, and, vice-versa, when the number of fundamentalists is greater than the number of interacting traders, absolute log-returns are characterised by an exponential distribution.
Keywords
- Stock Market
- Exponential Distribution
- Asset Price
- Complementary Cumulative Distribution Function
- Noise Trader
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. Mandelbrot, J. Business, 36, 34 (1965).
E.F. Fama, J. Business, 38, 35 (1965).
P. Gopikrishnan, et. al, Phys. Rev., 5305 E60 (1999).
V. Plerou, et. al., Phys. Rev., E60, 6519 (1999).
Y. Liu, et. al., Phys. Rev. E60, 1390 (1999).
P. Cizeau, et. Al., Physica A245, 437 (1997).
P. Bak, M. Paczuski and M. Shubik, Physica A246, 430 (1997).
D. Challet and Y.-C. Zhang, Physica A246, 407 (1997).
R. Cont and J. P. Bouchaud, Macroeconomic Dynamics 4, 170 (2000).
T. Lux, and M. Marchesi, Nature 397, 498 (1999).
D. Stauffer and D. Sornette, Physica A271, 496 (1999).
D. Chowdhury and D. Stauffer, Eur. Phys. J. B8, 477 (1999).
G. Iori, Int. Mod. Phys. C10, 1149 (1999).
D. Sornette, Physica A284, 355 (2000).
B.M. Roehner and D. Sornette, Eur. Phys. J. B16, 729 (2000).
S. Bornholdt, Int. J. Mod. Phys. C12 667 (2001).
A. Krawiecki, J.A. Holyst and D. Helbing, Phys. Rev. Lett. 89, 158701 (2002).
T. Kaizoji, Inflation and deflation in financial markets, (2003) available from http://arxiv.org/abs/cond-mat/0401140.
T. Kaizoji and M. Kaizoji, Advances in Complex Systems 6(3) (2003) 1.
T. Kaizoji and M. Kaizoji, Modeling absolute log-returns, unpublished paper (2003).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kaizoji, T. (2005). Statistical Properties of Absolute Log-Returns and a Stochastic Model of Stock Markets with Heterogeneous Agents. In: Lux, T., Samanidou, E., Reitz, S. (eds) Nonlinear Dynamics and Heterogeneous Interacting Agents. Lecture Notes in Economics and Mathematical Systems, vol 550. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27296-8_16
Download citation
DOI: https://doi.org/10.1007/3-540-27296-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22237-8
Online ISBN: 978-3-540-27296-0
eBook Packages: Business and EconomicsEconomics and Finance (R0)