A GENERAL ORNSTEIN–UHLENBECK STOCHASTIC VOLATILITY MODEL WITH LÉVY JUMPS

Karl Friedrich Hofmann () and Thorsten Schulz ()
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Karl Friedrich Hofmann: Deloitte & Touche GmbH, Kurfürstendamm 23, 10719 Berlin, Germany
Thorsten Schulz: Technische Universität München, Parkring 11, 85748 Garching-Hochbrück, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 08, 1-23

Abstract: We present a general class of stochastic volatility models with jumps where the stochastic variance process follows a Lévy-driven Ornstein–Uhlenbeck (OU) process and the jumps in the log-price process follow a Lévy process. This financial market model is a true extension of the Barndorff-Nielsen–Shephard (BNS) model class and can establish a weak link between log-price jumps and volatility jumps. Furthermore, we investigate the weak-link Γ-OU-BNS model as a special case, where we calculate the characteristic function of the logarithmic price in closed form. The classical Γ-OU-BNS model can be obtained as a limit of weak-link Γ-OU-BNS models in the Skorokhod topology. We highlight that the weak-link property may be a useful model extension in the case of pricing barrier options.

Keywords: Barndorff-Nielsen–Shephard model; stochastic volatility; jump-diffusion model; time change; Lévy processes (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:19:y:2016:i:08:n:s0219024916500448

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DOI: 10.1142/S0219024916500448

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