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Proceedings Paper

Asymmetry and multifractality in finance with an application to option smiles
Author(s): Benoit Pochart
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Paper Abstract

We briefly review the main stylized facts observed in financial markets and show how a multifractal process naturally captures those effects. In particular we generalize the construction of the multifractal random walk (MRW) due to Bacry, Delour and Muzy to take into account the asymmetric character of the financial returns. We show how one can include in this class of models the observed correlation between past returns and future volatilities, in such a way that the scale invariance properties of the MRW are preserved. Explicit scaling exponents are computes and are shown to behave differently for even and odd moments. We illustrate the usefulness of this "skewed" MRW by computing the resulting shape of the volatility smiles generated by such a process. A large variety of smile surfaces can be reproduced.

Paper Details

Date Published: 23 May 2005
PDF: 11 pages
Proc. SPIE 5848, Noise and Fluctuations in Econophysics and Finance, (23 May 2005); doi: 10.1117/12.609359
Show Author Affiliations
Benoit Pochart, EVA Funds (United States)

Published in SPIE Proceedings Vol. 5848:
Noise and Fluctuations in Econophysics and Finance
Derek Abbott; Jean-Philippe Bouchaud; Xavier Gabaix; Joseph L. McCauley, Editor(s)

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