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Processus multifractals en finance et valorisation d'options par minimisation de risques extrêmes.

Abstract : In a first part, after having recalled the main characteristics of financial time series, and especially the existence of long range non-linear correlations and of a persistent asymmetry, we show the relevance of multifractal processes for the modelling of such stylised facts. The constructions recently proposed in the literature remain however exclusively symmetric and we show how to introduce asymmetry in these models without losing their scaling laws. It is then possible to catch the phenomenon of volatility smile. In a second part we propose a numerical method for the pricing and hedging of options in incomplete markets. Furthermore our algorithm can be easily extended to take into account other market imperfections like transaction costs.
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https://pastel.archives-ouvertes.fr/pastel-00000704
Contributor : Ecole Polytechnique <>
Submitted on : Wednesday, July 21, 2010 - 9:28:27 AM
Last modification on : Friday, January 10, 2020 - 3:42:10 PM
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Benoit Pochart. Processus multifractals en finance et valorisation d'options par minimisation de risques extrêmes.. Mathématiques [math]. Ecole Polytechnique X, 2003. Français. ⟨pastel-00000704⟩

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