The ups and downs of the renormalization group applied to financial time series
Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently devised 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 Levy 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. 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.
|Date of creation:||26 Jul 2008|
|Date of revision:|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 70-86.
- R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
- Jean-Philippe Bouchaud & Marc Potters & Martin Meyer, 1999. "Apparent multifractality in financial time series," Science & Finance (CFM) working paper archive 9906347, Science & Finance, Capital Fund Management.
- Lisa Borland, 2002. "Option Pricing Formulas based on a non-Gaussian Stock Price Model," Papers cond-mat/0204331, arXiv.org, revised Sep 2002.
- Paul Lynch & Gilles Zumbach, 2003. "Market heterogeneities and the causal structure of volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 320-331.
- Laurent-Emmanuel Calvet & Benoît B. Mandelbrot & Adlai J. Fisher, 2011.
"A Multifractal Model of Asset Returns,"
- Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1999. "A Multifractal Model of Assets Returns," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-072, New York University, Leonard N. Stern School of Business-.
- Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
- 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.
- 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.
- 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;EDP Sciences, vol. 55(4), pages 453-459, 02.
- 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.
- S. Drozdz & M. Forczek & J. Kwapien & P. Oswiecimka & R. Rak, 2007. "Stock market return distributions: from past to present," Papers 0704.0664, arXiv.org.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:9770. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.