Stochastic modeling of fat-tailed probabilities of foreign exchange rates

  • Authors:

  • Mathias Karth;Joachim Peinke

  • Affiliations:

  • Fachbereich Physik, Carl-von-Ossietzky-University of Oldenburg, D-26111 Oldenburg, Germany;Fachbereich Physik, Carl-von-Ossietzky-University of Oldenburg, D-26111 Oldenburg, Germany

  • Venue:
  • Complexity - Complex Adaptive systems: Part I
  • Year:
  • 2002

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Abstract

In a recent work (Renner, C; Peinke, J.; Friedrich, R. Physica A 2001, 298, 211-217) it has been shown that the statistics of price changes on foreign-exchange rates measured by increments can be characterized completely by a Fokker-Planck equation. The explicit form of this Fokker-Planck equation was deduced directly from empirical data. Here we show that this result does not hold only for one specific construction of price changes by increments but also for returns and logarithmic returns, which are commonly used to quantify fluctuations in financial time-series over different time horizons. For all these quantities (increment and both kinds of returns) an explicit Fokker-Planck equation is presented and a verification of the quality of this description is shown by the reproduction of fat-tailed probability density functions for different time scales. We propose this method as a generalization of multifractal analysis.