Multi-Fractality in Foreign Currency Markets
34 Pages Posted: 8 Jul 2015
Date Written: July 7, 2015
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.
Keywords: exponent of Hurst; fractional Brownian motion; multi-fractal market hypothesis; Pareto-Levy stable process; R/S analysis
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