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A contribution to the systematics of stochastic volatility models

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  • Frantisek Slanina

Abstract

We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can assume also an algebraic decay, in the family of models which we call ``GARCH''-type. The intermediate regime is found in the exponential Ornstein-Uhlenbeck process. We calculate also the decay of the autocorrelation function of volatility.

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  • Frantisek Slanina, 2010. "A contribution to the systematics of stochastic volatility models," Papers 1009.2696, arXiv.org.
  • Handle: RePEc:arx:papers:1009.2696
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    File URL: http://arxiv.org/pdf/1009.2696
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    Cited by:

    1. Cassidy, Daniel T. & Hamp, Michael J. & Ouyed, Rachid, 2010. "Pricing European options with a log Student’s t-distribution: A Gosset formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5736-5748.
    2. Wei, Yu, 2012. "Forecasting volatility of fuel oil futures in China: GARCH-type, SV or realized volatility models?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5546-5556.

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