Markov properties of high frequency exchange rate data

Details Markov properties of high frequency exchange rate data Markov properties of high frequency exchange rate data

2001-02-27

arxiv.org/abs/cond-mat/0102494v2

Physics

Condensed Matter

Statistical Mechanics

29 pages, 19 eps figures, misprints corrected, under consideration for publication in Physica A

Scientific paper

10.1016/S0378-4371(01)00269-2

We present a stochastic analysis of a data set consisiting of 10^6 quotes of the US Doller - German Mark exchange rate. Evidence is given that the price changes x(tau) upon different delay times tau can be described as a Markov process evolving in tau. Thus, the tau-dependence of the probability density function (pdf) p(x) on the delay time tau can be described by a Fokker-Planck equation, a gerneralized diffusion equation for p(x,tau). This equation is completely determined by two coefficients D_{1}(x,tau) and D_{2}(x,tau) (drift- and diffusion coefficient, respectively). We demonstrate how these coefficients can be estimated directly from the data without using any assumptions or models for the underlying stochastic process. Furthermore, it is shown that the solutions of the resulting Fokker-Planck equation describe the empirical pdfs correctly, including the pronounced tails.

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