Multi-fractality in foreign currency markets

Several empirical studies have shown the inadequacy of the standard Brownian motion (sBm) as a model of asset returns. To correct for this evidence some authors have conjectured that asset returns may be independently and identically Pareto-Lévy stable (PLs) distributed, whereas others have asserted that asset returns may be identically - but not independently - fractional Brownian motion (fBm) distributed with Hurst exponents, in both cases, that differ from 0.5. In this article we empirically explore such non-standard assumptions for both spot and (nearby) futures returns for five foreign currencies: the British Pound, the Canadian Dollar, the German Mark, the Swiss Franc, and the Japanese Yen.

Several empirical studies have shown the inadequacy of the standard Brownian motion as a model of asset returns. To correct for this evidence, some authors have conjectured that asset returns may be independently and identically Pareto-Lévy stable distributed, whereas others have asserted that asset returns may be identically - but not independetly - fractional Brownian motion distributed with Hurst exponent, in both cases, that differes from 0.5. In this article we empirically explore such non-standard assumptions for both spot and (nearby) futures returns for five foreign currencies: the British Pound, the Canadian Dollar, the German Mark, the Swiss Franc, and the Japanese Yen.