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

28 Pages Posted: 29 Jul 2008 Last revised: 20 Jul 2009

See all articles by Damien Challet

Damien Challet

CentraleSupélec; Encelade Capital SA

Pier Paolo Peirano

Capital Fund Management

Date Written: July 29, 2008


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 Lévy 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.

Keywords: Stylized Facts, Student Processes, Hyperbolic Distributions, Wiener Process Mixtures

JEL Classification: C4, G10

Suggested Citation

Challet, Damien and Peirano, Pier Paolo, The Ups and Downs of Modeling Financial Time Series with Wiener Process Mixtures (July 29, 2008). Available at SSRN: or

Damien Challet

CentraleSupélec ( email )

3, rue Joliot-Curie
Gif-sur-Yvette, 91192

Encelade Capital SA ( email )

Chemin du Bochet 8
Sulpice, 1025

Pier Paolo Peirano (Contact Author)

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007

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