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Forecasting volatility with the multifractal random walk model

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
22
Number
1
Publisher
Wiley
Pages
83-108
Publication identifier
http://dx.doi.org/10.1111/j.1467-9965.2010.00458.x
Metadata
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Author(s)
Duchon, Jean
Robert, Raoul
Vargas, Vincent
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

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