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Filtering a nonlinear stochastic volatility model

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Abstract

We introduce a class of stochastic volatility models whose parameters are modulated by a hidden nonlinear dynamical system. Our aim is to incorporate the impact of economic cycles, or business cycles, into the long-term behavior of volatility dynamics. We develop a discrete-time nonlinear filter for the estimation of the hidden volatility and the nonlinear dynamical system based on return observations. By exploiting the technique of a reference probability measure we derive filters for the hidden volatility and the nonlinear dynamical system.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia

    Robert J. Elliott

  2. Haskayne School of Business, University of Calgary, Calgary, Alberta, Canada

    Robert J. Elliott

  3. Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW, 2109, Australia

    Tak Kuen Siu

  4. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Eric S. Fung

Authors
  1. Robert J. Elliott
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  2. Tak Kuen Siu
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  3. Eric S. Fung
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Correspondence to Robert J. Elliott.

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Elliott, R.J., Siu, T.K. & Fung, E.S. Filtering a nonlinear stochastic volatility model. Nonlinear Dyn 67, 1295–1313 (2012). https://doi.org/10.1007/s11071-011-0069-4

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  • DOI: https://doi.org/10.1007/s11071-011-0069-4

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