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Baldovin-Stella stochastic volatility process and Wiener process mixtures

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Author Info

  • Pier Paolo Peirano

    (CFM - Capital Fund Management - Capital Fund Management)

  • Damien Challet

    ()
    (MAS - Mathématiques Appliquées aux Systèmes - EA 4037 - Ecole Centrale Paris)

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.

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number hal-00734355.

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Date of creation: 06 Aug 2012
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Publication status: Published, Eur. Phys. J. B, 2012, 85, 8, 276
Handle: RePEc:hal:journl:hal-00734355

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00734355
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Related research

Keywords: Stochastic volatility model; long memory; stylized fact; fat tails;

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  1. Drożdż, S. & Forczek, M. & Kwapień, J. & Oświe¸cimka, P. & Rak, R., 2007. "Stock market return distributions: From past to present," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 59-64.
  2. Bacry, Emmanuel & Kozhemyak, Alexey & Muzy, Jean-François, 2006. "Are asset return tail estimations related to volatility long-range correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 119-126.
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  12. Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 70-86.
  13. Michel Vellekoop & Hans Nieuwenhuis, 2007. "On option pricing models in the presence of heavy tails," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 563-573.
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Cited by:
  1. Fulvio Baldovin & Massimiliano Caporin & Michele Caraglio & Attilio Stella & Marco Zamparo, 2013. "Option pricing with non-Gaussian scaling and infinite-state switching volatility," Papers 1307.6322, arXiv.org, revised May 2014.

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