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A contribution to the systematics of stochastic volatility models

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  • Slanina, František

Abstract

We systematically compare 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 also assume 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 also calculate the decay of the autocorrelation function of volatility.

Suggested Citation

  • Slanina, František, 2010. "A contribution to the systematics of stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3230-3239.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:16:p:3230-3239
    DOI: 10.1016/j.physa.2010.03.044
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    1. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169, January.
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    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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