Multifractal Random Walks With Fractional Brownian Motion via Malliavin Calculus

Author

Fauth, Alexis ; Tudor, Ciprian A.

Author_Institution

SAMM, Univ. de Pantheon-Sorbonne Paris 1, Paris, France

Volume

60

Issue

3

fYear

2014

fDate

Mar-14

Firstpage

1963

Lastpage

1975

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 for financial modeling that captures the main properties observed in the empirical data, including the leverage effect. We illustrate our result by numerical simulations.

Keywords

Brownian motion; numerical analysis; pricing; share prices; stochastic processes; time series; Malliavin calculus; continuous time model; cotton price; dependent fractional Brownian motion; financial modeling; financial stock price time series; infinitely divisible noise; leverage effect; multifractal random walks; numerical simulations; Biological system modeling; Brownian motion; Calculus; Fractals; Mathematical model; Noise; Stochastic processes; Fractional Brownian motion; Malliavin calculus; high frequency financial data; infinitely divisible cascades; leverage effect; multifractal random walk; scaling;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2013.2296785

Filename

6698302