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The Ups and Downs of Modeling Financial Time Series with Wiener Process Mixtures

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Damien Challet
Pier Paolo Peirano

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Abstract

Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a way to build a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated L\'evy distributions; we also show that the analytic tractability of the model extends to the larger class of symmetric generalized hyperbolic distributions and provide a full computation of their multivariate characteristic functions; more generally, the stochastic processes arising in this framework are representable as mixtures of Wiener processes. The Baldovin and Stella model, while mimicking well volatility relaxation phenomena such as the Omori law, fails to reproduce other stylized facts such as the leverage effect or some time reversal asymmetries. We discuss how to modify the dynamics of this process in order to reproduce real data more accurately.

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File URL: http://arxiv.org/abs/0807.4163
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0807.4163.

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Date of creation: Jul 2008
Date of revision: Jul 2009
Handle: RePEc:arx:papers:0807.4163

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  1. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation, Yale University. [Downloadable!]
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  2. Lisa Borland, 2002. "Option Pricing Formulas based on a non-Gaussian Stock Price Model," Quantitative Finance Papers cond-mat/0204331, arXiv.org, revised Sep 2002. [Downloadable!]
  3. S. Drozdz & M. Forczek & J. Kwapien & P. Oswiecimka & R. Rak, 2007. "Stock market return distributions: from past to present," Quantitative Finance Papers 0704.0664, arXiv.org. [Downloadable!]
  4. Dreier, I. & Kotz, S., 2002. "A note on the characteristic function of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 221-224, April. [Downloadable!] (restricted)
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