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A Multifractal Model of Assets Returns

Authors: Calvet, Laurent
Fisher, Adlai
Keywords: Multifractal Model of Asset Returns;Compound Stochastic Process;Time Deformation;Scaling;Self-Similarity;Multifractal Spectrum;Stochastic Volatility
Issue Date: 10-Nov-1999
Series/Report no.: FIN-99-072
Abstract: 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.
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