Exponentially Damped Lévy Flights, Multiscaling, and Exchange Rates

Raul Matsushita, University of Brasilia
Iram Gleria, University of Alagoas
Annibal Figueiredo, University of Brasilia
Rathie Rathie, University of Brasilia
Sergio Da Silva, Federal University of Rio Grande Do Sul

Abstract

We employ our previously suggested exponentially damped Lévy flight to study the multiscaling properties of 30 daily exchange rates against the US dollar together with a fictitious euro-dollar rate. Though multiscaling is not theoretically seen in either stable Levy processes or abruptly truncated Levy flights, it is even characteristic of smoothly truncated Levy flights. We have already defined a class of "quasi-stable" processes in connection with the finding that single scaling is pervasive among the dollar price of foreign currencies. Here we show that the same goes as far as multiscaling is concerned. Our novel findings reinforce the case for Levy flights in the modeling of financial prices.