Department of Economics and Business Economics

Stochastic volatility and stochastic leverage

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  • Rp09 20

    Final published version, 456 KB, PDF document

  • Almut Veraart
  • Luitgard A. M. Veraart, Institut für Stochastik, Universität Karlsruhe, Germany
  • School of Economics and Management
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.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for økonomi, Aarhus Universitet
Number of pages49
Publication statusPublished - 2009

    Research areas

  • Stochastic volatility, volatility of volatility, stochastic correlation, leverage effect, Jacobi process, Ornstein–Uhlenbeck process, square root diffusion, Lévy process, Heston

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