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A note on stochastic volatility, GARCH models, and hyperbolic distributions

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  • Jaschke, Stefan R.

Abstract

We establish a relation between stochastic volatility models and the class of generalized hyperbolic distributions. These distributions have been found to fit exceptionally well to the empirical distribution of stock returns. We review the background of hyperbolic distributions and prove stationary distributions of certain GARCH-type models to be generalized hyperbolic.

Suggested Citation

  • Jaschke, Stefan R., 1997. "A note on stochastic volatility, GARCH models, and hyperbolic distributions," SFB 373 Discussion Papers 1998,23, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199823
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
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