Baldovin-Stella stochastic volatility process and Wiener process mixtures

Pier Paolo Peirano and Damien Challet

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Abstract: Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently proposed a powerful and consistent 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 and 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, we show that the stochastic processes arising in this framework are representable as mixtures of Wiener processes. The basic 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: Stochastic volatility model; long memory; stylized fact; fat tails (search for similar items in EconPapers)
Date: 2012-08-06
New Economics Papers: this item is included in nep-ets
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Published in The European Physical Journal B: Condensed Matter and Complex Systems, 2012, 85 (8), pp.276. ⟨10.1140/epjb/e2012-30134-y⟩

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Journal Article: Baldovin-Stella stochastic volatility process and Wiener process mixtures (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00734355

DOI: 10.1140/epjb/e2012-30134-y

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