Forecasting volatility with the multifractal random walk model

Duchon, Jean; Robert, Raoul; Vargas, Vincent

Duchon, Jean; Robert, Raoul; Vargas, Vincent (2012), Forecasting volatility with the multifractal random walk model, Mathematical Finance, 22, 1, p. 83-108. http://dx.doi.org/10.1111/j.1467-9965.2010.00458.x

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00220402/en/

Date

2012

Journal name

Mathematical Finance

Volume

Number

Publisher

Wiley

Pages

83-108

Abstract (EN)

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.

Subjects / Keywords

Random measures; Gaussian processes; Prediction theory; Multifractal processes