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Stochastic volatility and stochastic leverage

  • Almut E. D. Veraart

    ()

    (School of Economics and Management, Aarhus University and CREATES)

  • Luitgard A. M. Veraart

    ()

    (Institut für Stochastik, Universität Karlsruhe)

This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new models. Furthermore, we give a detailed account on statistical properties of the new models.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-20.

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Length: 49
Date of creation: 19 May 2009
Date of revision:
Handle: RePEc:aah:create:2009-20
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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