Baldovin-Stella stochastic volatility process and Wiener process mixtures
AbstractStarting 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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Date of creation: 06 Aug 2012
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Publication status: Published, Eur. Phys. J. B, 2012, 85, 8, 276
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Stochastic volatility model; long memory; stylized fact; fat tails;
Other versions of this item:
- P. Peirano & D. Challet, 2012. "Baldovin-Stella stochastic volatility process and Wiener process mixtures," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 85(8), pages 1-12, August.
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- 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.
- 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.
- S. Drozdz & M. Forczek & J. Kwapien & P. Oswiecimka & R. Rak, 2007. "Stock market return distributions: from past to present," Papers 0704.0664, arXiv.org.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
- F. Lillo, 2007. "Limit order placement as an utility maximization problem and the origin of power law distribution of limit order prices," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 55(4), pages 453-459, 02.
- Paul Lynch & Gilles Zumbach, 2003. "Market heterogeneities and the causal structure of volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 320-331.
- George Chang & James Feigenbaum, 2006. "A Bayesian analysis of log-periodic precursors to financial crashes," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 15-36.
- D. Sornette & Y. Malevergne & J. F. Muzy, 2002. "Volatility fingerprints of large shocks: Endogeneous versus exogeneous," Papers cond-mat/0204626, arXiv.org.
- R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
- J.-P. Bouchaud & M. Potters & M. Meyer, 2000. "Apparent multifractality in financial time series," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 13(3), pages 595-599, 02.
- repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
- Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 70-86.
- 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.
- D. Sornette, 2003. "Critical Market Crashes," Papers cond-mat/0301543, arXiv.org.
- 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.
- 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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