A multivariate multifractal model for return fluctuations

TL;DR

This paper reviews the Multifractal Random Walk model and extends it to a multivariate setting to better understand the complex correlations in financial return data across different assets and time scales.

Contribution

It introduces a multivariate extension of the MRW model, capturing both linear and non-linear correlations in multivariate financial time series.

Findings

The multivariate model reproduces empirical features of financial data.

It effectively captures long-range volatility correlations.

The approach models complex inter-asset dependencies.

Abstract

In this paper we briefly review the recently inrtroduced Multifractal Random Walk (MRW) that is able to reproduce most of recent empirical findings concerning financial time-series : no correlation between price variations, long-range volatility correlations and multifractal statistics. We then focus on its extension to a multivariate context in order to model portfolio behavior. Empirical estimations on real data suggest that this approach can be pertinent to account for the nature of both linear and non-linear correlation between stock returns at all time scales.