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Volatility in financial markets: stochastic models and empirical results

Author

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  • Miccichè, Salvatore
  • Bonanno, Giovanni
  • Lillo, Fabrizio
  • Mantegna, Rosario N

Abstract

We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pdf in the region of low values of volatility whereas the Hull and White model better approximates the empirical pdf for large values of volatility. Both models fail in describing the empirical pdf over a moderately large volatility range.

Suggested Citation

  • Miccichè, Salvatore & Bonanno, Giovanni & Lillo, Fabrizio & Mantegna, Rosario N, 2002. "Volatility in financial markets: stochastic models and empirical results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 756-761.
  • Handle: RePEc:eee:phsmap:v:314:y:2002:i:1:p:756-761
    DOI: 10.1016/S0378-4371(02)01187-1
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    Cited by:

    1. Ralf Remer & Reinhard Mahnke, 2004. "Application of the heston and hull-white models to german dax data," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 685-693.
    2. Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010. "Pricing bounds for discrete arithmetic Asian options under Lévy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207.
    3. Lisa Borland & Jean-Philippe Bouchaud & Jean-Francois Muzy & Gilles Zumbach, 2005. "The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond," Science & Finance (CFM) working paper archive 500061, Science & Finance, Capital Fund Management.
    4. feng dai, 2004. "The Partial Distribution: Definition, Properties and Applications in Economy," Econometrics 0403008, University Library of Munich, Germany.
    5. G. L. Buchbinder & K. M. Chistilin, 2006. "Multiple time scales and the empirical models for stochastic volatility," Papers physics/0611048, arXiv.org.
    6. Miccichè, S., 2016. "Understanding the determinants of volatility clustering in terms of stationary Markovian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 186-197.
    7. DAI & Feng QIN & Zifu, 2005. "DF Structure Models for Options Pricing," The IUP Journal of Applied Economics, IUP Publications, vol. 0(6), pages 61-77, November.
    8. Linden, Mikael, 2005. "Estimating the distribution of volatility of realized stock returns and exchange rate changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 573-583.
    9. Aki-Hiro Sato & Paolo Tasca & Takashi Isogai, 2019. "Dynamic Interaction Between Asset Prices and Bank Behavior: A Systemic Risk Perspective," Computational Economics, Springer;Society for Computational Economics, vol. 54(4), pages 1505-1537, December.
    10. Lisa Borland & Jean-Philippe Bouchaud & Jean-Francois Muzy & Gilles Zumbach, 2005. "The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond," Papers cond-mat/0501292, arXiv.org.
    11. Renò, Roberto & Rizza, Rosario, 2003. "Is volatility lognormal? Evidence from Italian futures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 620-628.
    12. Meudt, Frederik & Schmitt, Thilo A. & Schäfer, Rudi & Guhr, Thomas, 2016. "Equilibrium pricing in an order book environment: Case study for a spin model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 228-235.
    13. Feng Dai & Lin Liang, 2005. "The Advance in Partial Distribution£ºA New Mathematical Tool for Economic Management," Econometrics 0508001, University Library of Munich, Germany.
    14. L. Borland & J. -Ph. Bouchaud, 2005. "On a multi-timescale statistical feedback model for volatility fluctuations," Papers physics/0507073, arXiv.org.
    15. Frederik Meudt & Thilo A. Schmitt & Rudi Schafer & Thomas Guhr, 2015. "Equilibrium Pricing in an Order Book Environment: Case Study for a Spin Model," Papers 1502.01125, arXiv.org.
    16. Giacomo Bormetti & Valentina Cazzola & Danilo Delpini, 2009. "Option pricing under Ornstein-Uhlenbeck stochastic volatility: a linear model," Papers 0905.1882, arXiv.org, revised May 2010.
    17. Li, Wenwei & Hommel, Ulrich & Paterlini, Sandra, 2018. "Network topology and systemic risk: Evidence from the Euro Stoxx market," Finance Research Letters, Elsevier, vol. 27(C), pages 105-112.
    18. Bernardo Spagnolo & Davide Valenti, 2008. "Volatility Effects on the Escape Time in Financial Market Models," Papers 0810.1625, arXiv.org.
    19. Li, Chao & Shang, Pengjian, 2018. "Complexity analysis based on generalized deviation for financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 118-128.
    20. Buchbinder, G.L. & Chistilin, K.M., 2007. "Multiple time scales and the empirical models for stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 168-178.

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    Keywords

    Econophysics; Stochastic processes; Volatility;

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