Abstract : We introduce a Multifractal Random Walk (MRW) defined as a stochastic integral of an infinitely divisible noise with respect to a Hermite process. Hermite processes are self-similar stochastic processes with stationary increments and exhibit long-range dependence. We study the existence of the Hermite MRW and its properties. We propose a continuous time financial model that captures the multifractal properties observed in the empirical data. We also present a numerical analysis of our results.
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Contributor : Ciprian Tudor <>
Submitted on : Tuesday, May 23, 2017 - 3:59:52 PM Last modification on : Tuesday, January 19, 2021 - 11:08:40 AM
Alexis Fauth, Ciprian A. Tudor. Multifractal random walk driven by a Hermite process. Handbook of high-frequency trading and modeling in finance, Wiley Handb. Finance Eng. Econom., Wiley, Hoboken, NJ, 2016. ⟨hal-01526873⟩