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Deterministic and stochastic influences on Japan and US stock and foreign exchange markets. A Fokker-Planck approach

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  • K. Ivanova
  • M. Ausloos
  • H. Takayasu

Abstract

The evolution of the probability distributions of Japan and US major market indices, NIKKEI 225 and NASDAQ composite index, and $JPY/DEM$ and $DEM/USD$ currency exchange rates is described by means of the Fokker-Planck equation (FPE). In order to distinguish and quantify the deterministic and random influences on these financial time series we perform a statistical analysis of their increments $\Delta x(\Delta(t))$ distribution functions for different time lags $\Delta(t)$. From the probability distribution functions at various $\Delta(t)$, the Fokker-Planck equation for $p(\Delta x(t), \Delta(t))$ is explicitly derived. It is written in terms of a drift and a diffusion coefficient. The Kramers-Moyal coefficients, are estimated and found to have a simple analytical form, thus leading to a simple physical interpretation for both drift $D^{(1)}$ and diffusion $D^{(2)}$ coefficients. The Markov nature of the indices and exchange rates is shown and an apparent difference in the NASDAQ $D^{(2)}$ is pointed out.

Suggested Citation

  • K. Ivanova & M. Ausloos & H. Takayasu, 2003. "Deterministic and stochastic influences on Japan and US stock and foreign exchange markets. A Fokker-Planck approach," Papers cond-mat/0301268, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0301268
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    References listed on IDEAS

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    4. Baviera, Roberto & Pasquini, Michele & Serva, Maurizio & Vergni, Davide & Vulpiani, Angelo, 2002. "Antipersistent Markov behavior in foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(3), pages 565-576.
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    Cited by:

    1. Miśkiewicz, Janusz, 2012. "Economy with the time delay of information flow—The stock market case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1388-1394.

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