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

Summary

The evolution of the probability distributions of Japan and US major market indices, NIKKEI 225 and NASDAQ composite index, and JPY/DF,M 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 Δx(Δ(t)) distribution functions for different time lags Δ(t). From the probability distribution functions at variousΔ(t),the Fokker-Planck equation for p(Δx(t), Δ(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 driftD ⁽¹⁾ and diffusionD ⁽²⁾coefficients. The Markov nature of the indices and exchange rates is shown and an apparent difference in the NASDAQD ⁽²⁾ is pointed out.