A Multifractal Model of Assets Returns

56 Pages Posted: 11 Nov 2008

See all articles by Laurent E. Calvet

Laurent E. Calvet

SKEMA Business School; CEPR

Adlai J. Fisher

University of British Columbia (UBC) - Sauder School of Business

Date Written: November 1999


This paper investigates the Multifractal Model of Asset Returns, a continuous-time process that incorporates the thick tails and volatility persistence exhibited by many financial time series. The model is constructed by compounding a Brownian Motion with a multifractal time-deformation process. Return moments scale as a power law of the time horizon, a property confirmed for Deutschemark / U.S. Dollar exchange rates and several equity series. The model implies semi-martingale prices and thus precludes arbitrage in a standard two-asset economy. Volatility has long-memory, and the highest finite moment of returns can have any value greater than two. The local variability of the process is characterized by a renormalized probability density of local Hölder exponents. Unlike standard models, multifractal paths contain a multiplicity of these exponents within any time interval. We develop an estimation method, and infer a parsimonious generating mechanism for the exchange rate series. Simulated samples replicate the moment-scaling found in the data.

Keywords: Multifractal Model of Asset Returns, Compound Stochastic Process, Time Deformation, Scaling, Self-Similarity, Multifractal Spectrum, Stochastic Volatility

Suggested Citation

Calvet, Laurent E. and Fisher, Adlai J., A Multifractal Model of Assets Returns (November 1999). NYU Working Paper No. FIN-99-072, Available at SSRN: https://ssrn.com/abstract=1299397

Laurent E. Calvet (Contact Author)

SKEMA Business School ( email )

5 Quai Marcel Dassault
Suresnes, 92150

CEPR ( email )

33 Great Sutton Street
London, EC1V 0DX
United Kingdom

Adlai J. Fisher

University of British Columbia (UBC) - Sauder School of Business ( email )

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Vancouver, BC V6T 1Z2
604-822-8331 (Phone)
604-822-4695 (Fax)

HOME PAGE: http://finance.sauder.ubc.ca/~fisher

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