A multifractal approach towards inference in finance

TL;DR

This paper develops new inference tools for the multifractal random walk model in finance, enabling improved volatility forecasting and density estimation, demonstrated on Oslo Stock Exchange data.

Contribution

It introduces formulas and methods for smoothing, filtering, and forecasting in the multifractal framework, enhancing financial inference techniques.

Findings

Multifractal volatility forecasts show richer structures than stochastic volatility models.

New formulas enable effective smoothing and filtering in multifractal models.

Application to real stock data demonstrates practical utility.

Abstract

We introduce tools for inference in the multifractal random walk introduced by Bacry et al. (2001). These tools include formulas for smoothing, filtering and volatility forecasting. In addition, we present methods for computing conditional densities for one- and multi-step returns. The inference techniques presented in this paper, including maximum likelihood estimation, are applied to data from the Oslo Stock Exchange, and it is observed that the volatility forecasts based on the multifractal random walk have a much richer structure than the forecasts obtained from a basic stochastic volatility model.