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Journal Articles IEEE Transactions on Information Theory Year : 2014

Multifractal random walks with fractional Brownian motion via Malliavin calculus

Abstract

We introduce a Multifractal Random Walk (MRW) defined as a stochastic integral of an infinitely divisible noise with respect to a dependent fractional Brownian motion. Using the techniques of the Malliavin calculus, we study the existence of this object and its properties. We then propose a continuous time model in finance that captures the main properties observed in the empirical data, including the leverage effect. We illustrate our result by numerical simulations.
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Dates and versions

hal-00734180 , version 1 (20-09-2012)

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Alexis Fauth, Ciprian Tudor. Multifractal random walks with fractional Brownian motion via Malliavin calculus. IEEE Transactions on Information Theory, 2014, 60 (3), pp.12. ⟨hal-00734180⟩
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