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On a multi-timescale statistical feedback model for volatility fluctuations

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  • Lisa Borland

    (Evnine-Vaughan Associates, Inc.)

  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

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    Abstract

    We study, both analytically and numerically, an ARCH-like, multiscale model of volatility, which assumes that the volatility is governed by the observed past price changes on different time scales. With a power-law distribution of time horizons, we obtain a model that captures most stylized facts of financial time series: Student-like distribution of returns with a power-law tail, long-memory of the volatility, slow convergence of the distribution of returns towards the Gaussian distribution, multifractality and anomalous volatility relaxation after shocks. At variance with recent multifractal models that are strictly time reversal invariant, the model also reproduces the time assymmetry of financial time series: past large scale volatility influence future small scale volatility. In order to quantitatively reproduce all empirical observations, the parameters must be chosen such that our model is close to an instability, meaning that (a) the feedback effect is important and substantially increases the volatility, and (b) that the model is intrinsically difficult to calibrate because of the very long range nature of the correlations. By imposing the consistency of the model predictions with a large set of different empirical observations, a reasonable range of the parameters value can be determined. The model can easily be generalized to account for jumps, skewness and multiasset correlations.

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    Bibliographic Info

    Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500059.

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    Date of creation: Jul 2005
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    Handle: RePEc:sfi:sfiwpa:500059

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    1. Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
    2. D. Challet & A. Chessa & M. Marsili & Y. -C. Zhang, 2000. "From Minority Games to real markets," Papers cond-mat/0011042, arXiv.org.
    3. Fabrizio Lillo & Rosario N. Mantegna, 2001. "Power law relaxation in a complex system: Omori law after a financial market crash," Papers cond-mat/0111257, arXiv.org, revised Jun 2003.
    4. Josep Perello & Jaume Masoliver & Jean-Philippe Bouchaud, 2003. "Multiple time scales in volatility and leverage correlation: A stochastic volatility model," Science & Finance (CFM) working paper archive 50001, Science & Finance, Capital Fund Management.
    5. Andrew W. Lo, 1989. "Long-term Memory in Stock Market Prices," NBER Working Papers 2984, National Bureau of Economic Research, Inc.
    6. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
    7. Lisa Borland, 2002. "A theory of non-Gaussian option pricing," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 2(6), pages 415-431.
    8. Hommes, C.H., 2000. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," CeNDEF Working Papers 00-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    9. L. Borland & J. P. Bouchaud, 2004. "A Non-Gaussian Option Pricing Model with Skew," Papers cond-mat/0403022, arXiv.org, revised Mar 2004.
    10. Carl Chiarella & Xue-Zhong He, 2001. "Asset Price and Wealth Dynamics Under Heterogeneous Expectations," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 56, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Benoit Pochart & Jean-Philippe Bouchaud, 2002. "The skewed multifractal random walk with applications to option smiles," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 2(4), pages 303-314.
    12. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 73(1), pages 151-184, July.
    13. Adrian A. Dragulescu & Victor M. Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Papers cond-mat/0203046, arXiv.org, revised Nov 2002.
    14. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, Elsevier, vol. 1(1), pages 83-106, June.
    15. Geman, Hélyette & Carr, Peter & Madan, Dilip B. & Yor, Marc, 2003. "Stochastic Volatility for Levy Processes," Economics Papers from University Paris Dauphine 123456789/1392, Paris Dauphine University.
    16. Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 4(1), pages 70-86.
    17. Cars H. Hommes, 2001. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," Tinbergen Institute Discussion Papers 01-014/1, Tinbergen Institute.
    18. Lisa Borland & Jean-Philippe Bouchaud, 2004. "A non-Gaussian option pricing model with skew," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 4(5), pages 499-514.
    19. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    20. Benoit Pochard & Jean-Philippe Bouchaud, 2002. "The skewed multifractal random walk with applications to option smiles," Science & Finance (CFM) working paper archive 0204047, Science & Finance, Capital Fund Management.
    21. Laurent Calvet & Adlai Fisher, 1999. "Forecasting Multifractal Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires, New York University, Leonard N. Stern School of Business- 99-017, New York University, Leonard N. Stern School of Business-.
    22. Adrian Dragulescu & Victor Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 2(6), pages 443-453.
    23. A. Dragulescu & V. M. Yakovenko, 2002. "Probability distribution of returns in the Heston model with stochastic volatility," Computing in Economics and Finance 2002 127, Society for Computational Economics.
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