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The multivariate supOU stochastic volatility model

Author

Listed:
  • Ole Eiler Barndorff-Nielsen

    (Thiele Centre, Department of Mathematical Sciences & CREATES, Aarhus University)

  • Robert Stelzer

    (TUM Institute for Advanced Study & Zentrum Mathematik, Technische Universität München)

Abstract

Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order structure of the volatility, the log returns, as well as their “squares” are discussed in detail. Moreover, we give several examples in which long memory effects occur and study how the model as well as the simple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations. In particular, the models are shown to be preserved under invertible linear transformations. Finally, we discuss how (sup)OU stochastic volatility models can be combined with a factor modelling approach.

Suggested Citation

  • Ole Eiler Barndorff-Nielsen & Robert Stelzer, 2009. "The multivariate supOU stochastic volatility model," CREATES Research Papers 2009-42, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2009-42
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    File URL: https://repec.econ.au.dk/repec/creates/rp/09/rp09_42.pdf
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    References listed on IDEAS

    as
    1. Richard B. Olsen & Ulrich A. Müller & Michel M. Dacorogna & Olivier V. Pictet & Rakhal R. Davé & Dominique M. Guillaume, 1997. "From the bird's eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 95-129.
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    More about this item

    Keywords

    factor modelling; Lévy bases; linear transformations; long memory; Ornstein-Uhlenbeck type process; second order moment structure; stochastic volatility;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets

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