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

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

2003-01-15

arxiv.org/abs/cond-mat/0301268v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 5 figures; to appear in the Proceedings of the Proceedings of the Second Nikkei Symposium: Toward control of Economic

Scientific paper

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.

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