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Stochastic Volatility and Jumps Driven by Continuous Time Markov Chains

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  • Kyriakos Chourdakis

    (Queen Mary, University of London)

Abstract

This paper considers a model where there is a single state variable that drives the state of the world and therefore the asset price behavior. This variable evolves according to a multi-state continuous time Markov chain, as the continuous time counterpart of the Hamilton (1989) model. It derives the moment generating function of the asset log-price difference under very general assumptions about its stochastic process, incorporating volatility and jumps that can follow virtually any distribution, both of them being driven by the same state variable. For an illustration, the extreme value distribution is used as the jump distribution. The paper shows how GMM and conditional ML estimators can be constructed, generalizing Hamilton's filter for the continuous time case. The risk neutral process is constructed and contigent claim prices under this specification are derived, in the lines of Bakshi and Madan (2000). Finally, an empirical example is set up, to illustrate the potential benefits of the model.

Suggested Citation

  • Kyriakos Chourdakis, 2000. "Stochastic Volatility and Jumps Driven by Continuous Time Markov Chains," Working Papers 430, Queen Mary University of London, School of Economics and Finance.
    • Handle: RePEc:qmw:qmwecw:430
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    File URL: https://www.qmul.ac.uk/sef/media/econ/research/workingpapers/2000/items/wp430.pdf
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    References listed on IDEAS

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    Cited by:

    1. Yu Yang & Yonghong Wu & Benchawan Wiwatanapataphee, 2020. "Time-consistent mean–variance asset-liability management in a regime-switching jump-diffusion market," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(4), pages 401-427, December.
    2. Xie, Shuxiang, 2009. "Continuous-time mean-variance portfolio selection with liability and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 148-155, August.
    3. Cajueiro, Daniel Oliveira & Yoneyama, Takashi, 2004. "Optimal Portfolio and Consumption in a Switching Diffusion Market," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 24(2), November.

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    More about this item

    Keywords

    Option pricing; Markov chain; Moment generating function;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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