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.
https://hal.inria.fr/hal-01526873
Contributor : Ciprian Tudor
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Submitted on : Tuesday, May 23, 2017 - 3:59:52 PM
Last modification on : Tuesday, July 3, 2018 - 11:34:29 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〉
