Forecasting volatility with the multifractal random walk model

TL;DR

This paper develops a novel approach for forecasting volatility in the multifractal random walk model by introducing a limiting object that simplifies prediction formulas, enabling more reliable volatility forecasting and option pricing without estimating correlation length.

Contribution

It introduces a limiting object in a quotient space for the MRW model, providing precise prediction formulas that bypass the need to estimate correlation length T.

Findings

Effective volatility forecasting formulas derived

Applicable to option pricing without estimating average volatility

Improved robustness in volatility prediction

Abstract

We study the problem of forecasting volatility for the multifractal random walk model. In order to avoid the ill posed problem of estimating the correlation length T of the model, we introduce a limiting object defined in a quotient space; formally, this object is an infinite range logvolatility. For this object and the non limiting object, we obtain precise prediction formulas and we apply them to the problem of forecasting volatility and pricing options with the MRW model in the absence of a reliable estimate of the average volatility and T.