Multifractality in Foreign Currency Markets

28 Pages Posted: 17 Jan 2008

See all articles by Marco Corazza

Marco Corazza

Ca Foscari University of Venice - Dipartimento di Economia

A. (Tassos) G. Malliaris

Loyola University Chicago


The standard hypothesis concerning the behavior of asset returns states that they follow a random walk in discrete time or a Brownian motion in continuous time. The Brownian motion process is characterized by a quantity, called the Hurst exponent, which is related to some fractal aspects of the process itself. For a standard Brownian motion (sBm) this exponent is equal to 0.5. Several empirical studies have shown the inadequacy of the sBm. 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 paper 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. We assume that the Hurst exponent belongs to a suitable neighborhood of 0.5 that allows us to verify if the so-called Fractal Market Hypothesis (FMH) can be a "reasonable" generalization of the Efficient Market hypothesis. Furthermore, we also allow the Hurst exponent to vary over time which permits the generalization of the FMH into the MultiFractal Market Hypothesis (MFMH).

Keywords: Exponent of Hurst, multifractal market hypothesis, fractional Brownian motion,Pareto-Lévy stable process, statistical self-similarity, modified rescaled range (or R/S) analysis,periodogram-based approach, foreign currency markets

JEL Classification: A00

Suggested Citation

Corazza, Marco and Malliaris, A. (Tassos) G., Multifractality in Foreign Currency Markets. Multinational Finance Journal, Vol. 6, pp. 387-401, 2002, Available at SSRN:

Marco Corazza

Ca Foscari University of Venice - Dipartimento di Economia ( email )

Cannaregio 873
Venice, 30121

A. (Tassos) G. Malliaris (Contact Author)

Loyola University Chicago ( email )

16 E. Pearson Ave
Quinlan School of Business
Chicago, IL 60611
United States
312-915-6063 (Phone)

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