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A General Ornstein–Uhlenbeck Stochastic Volatility Model With Lévy Jumps

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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)

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.

Suggested Citation

  • Karl Friedrich Hofmann & Thorsten Schulz, 2016. "A General Ornstein–Uhlenbeck Stochastic Volatility Model With Lévy Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-23, December.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:08:n:s0219024916500448
    DOI: 10.1142/S0219024916500448
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