Stochastic volatility and stochastic leverage

Almut Veraart and Luitgard A. M. Veraart ()
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Luitgard A. M. Veraart: Institut für Stochastik, Universität Karlsruhe, Postal: Institut für Stochastik, Universität Karlsruhe (TH), 76128 Karlsruhe, GERMANY

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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.

Keywords: Stochastic volatility; volatility of volatility; stochastic correlation; leverage effect; Jacobi process; Ornstein–Uhlenbeck process; square root diffusion; Lévy process; Heston model; Barndorff-Nielsen & Shephard model (search for similar items in EconPapers)
JEL-codes: C1 C5 G0 G1 (search for similar items in EconPapers)
Pages: 49
Date: 2009-05-19
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Journal Article: Stochastic volatility and stochastic leverage (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2009-20

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