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A Class of Nonlinear Stochastic Volatility Models

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  • Yu, Jun
  • Yang, Zhenlin

Abstract

This paper proposes a class of stochastic volatility (SV) models which offers an alternative to the one introduced in Andersen (1994). The class encompasses all standard SV models that have appeared in the literature, including the well known lognormal model, and allows us to empirically test all standard specifications in a convenient way. We develop a likelihood-based technique for analyzing the class. Daily dollar/pound exchange rate data reject all the standard models and suggest evidence of nonlinear SV. An efficient algorithm is proposed to study the implications of this nonlinear SV on pricing currency options and it is found that the lognormal model overprices options.

Suggested Citation

  • Yu, Jun & Yang, Zhenlin, 2002. "A Class of Nonlinear Stochastic Volatility Models," Working Papers 203, Department of Economics, The University of Auckland.
    • Handle: RePEc:auc:wpaper:203
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    File URL: http://hdl.handle.net/2292/203
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    Cited by:

    1. Goodwin, Roger L, 2015. "Random Variables, Their Properties, and Deviational Ellipses: In Map Point and Excel, v 4.3," MPRA Paper 64863, University Library of Munich, Germany, revised 07 Jun 2015.
    2. Chen, Liyuan & Zerilli, Paola & Baum, Christopher F., 2019. "Leverage effects and stochastic volatility in spot oil returns: A Bayesian approach with VaR and CVaR applications," Energy Economics, Elsevier, vol. 79(C), pages 111-129.
    3. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    4. Zhang, Xibin & King, Maxwell L., 2008. "Box-Cox stochastic volatility models with heavy-tails and correlated errors," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 549-566, June.
    5. Goodwin, Roger L, 2014. "Random Variables, Their Properties, and Deviational Ellipses: In Map Point and Excel, v 4.0," MPRA Paper 64391, University Library of Munich, Germany, revised 15 May 2015.
    6. Kawakatsu, Hiroyuki, 2007. "Specification and estimation of discrete time quadratic stochastic volatility models," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 424-442, June.

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    Keywords

    Economics;

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