Multifractal random walks with fractional Brownian motion via Malliavin calculus
Probability
2012-09-24 v1
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.
Keywords
Cite
@article{arxiv.1209.4717,
title = {Multifractal random walks with fractional Brownian motion via Malliavin calculus},
author = {Alexis Fauth and Ciprian Tudor},
journal= {arXiv preprint arXiv:1209.4717},
year = {2012}
}