Statistical Investigation of Increments of Currency Rates Logarithms

TL;DR

This paper analyzes currency rate changes for 12 currencies against the Russian rouble, demonstrating that common models like geometric Brownian motion and inverse Gaussian increments are unsuitable, and highlighting behavioral differences across currencies and time periods.

Contribution

It provides a statistical assessment showing the inadequacy of standard models for currency rate dynamics and compares behaviors before and during the 2008 financial crisis.

Findings

Samuelson model is not suitable for currency rates

Inverse Gaussian model does not fit currency log-increments

Behavioral differences observed across currencies and time periods

Abstract

We consider the currency rates dynamics for 12 currencies, including dollar and euro, with respect to Russian rouble. We prove that the Samuelson model (geometric Brownian motion) is not suitable for this dynamics. We also prove that another model (with inverse Gaussian increments of logarithms) is not appropriate for this situation. We point out the difference in behavior of different currencies, and the difference in behavior before and during the financial crisis which began in 2008.