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A General Ornstein–Uhlenbeck Stochastic Volatility Model With Lévy Jumps

Author

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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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    References listed on IDEAS

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    Cited by:

    1. Zhenyu Cui & J. Lars Kirkby & Guanghua Lian & Duy Nguyen, 2017. "Integral Representation Of Probability Density Of Stochastic Volatility Models And Timer Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    2. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.

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