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Stochastic volatility and stochastic leverage

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Abstract

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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Authors and Affiliations

  1. CREATES, School of Economics and Management, Aarhus University, Building 1322, 8000, Aarhus C, Denmark

    Almut E. D. Veraart

  2. Department of Mathematics, Institute for Stochastics, Karlsruhe Institute of Technology, Kaiserstr. 89, 76133, Karlsruhe, Germany

    Luitgard A. M. Veraart

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  1. Almut E. D. Veraart
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  2. Luitgard A. M. Veraart
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Correspondence to Almut E. D. Veraart.

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Veraart, A.E.D., Veraart, L.A.M. Stochastic volatility and stochastic leverage. Ann Finance 8, 205–233 (2012). https://doi.org/10.1007/s10436-010-0157-3

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  • DOI: https://doi.org/10.1007/s10436-010-0157-3

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