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Stochastic volatility with an Ornstein-Uhlenbeck process: An extension

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  • Schöbel, Rainer
  • Zhu, Jianwei

Abstract

In this paper, we reexamine and extend the stochastic volatility model of Stein and Stein (1991) where volatility follows a mean-reversion Ornstein-Uhlenbeck process. Using Fourier inversion techniques we are able to allow for correlation between instan-taneous volatilities and the underlying stock returns. A closed-form pricing Solution for European options is derived and some numerical examples are given.

Suggested Citation

  • Schöbel, Rainer & Zhu, Jianwei, 1998. "Stochastic volatility with an Ornstein-Uhlenbeck process: An extension," Tübinger Diskussionsbeiträge 139, University of Tübingen, School of Business and Economics.
    • Handle: RePEc:zbw:tuedps:139
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    References listed on IDEAS

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    1. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
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    Cited by:

    1. Coppola, Mariarosaria & D’Amato, Valeria & Levantesi, Susanna, 2018. "An option pricing approach for measuring Solvency Capital Requirements in Insurance Industry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 717-728.
    2. Daouk, Hazem & Guo, Jie Qun, 2003. "Switching Asymmetric GARCH and Options on a Volatility Index," Working Papers 127187, Cornell University, Department of Applied Economics and Management.
    3. Ben-Zhang Yang & Xiaoping Lu & Guiyuan Ma & Song-Ping Zhu, 2020. "Robust Portfolio Optimization with Multi-Factor Stochastic Volatility," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 264-298, July.
    4. Leonardo Perotti & Lech A. Grzelak, 2021. "Fast Sampling from Time-Integrated Bridges using Deep Learning," Papers 2111.13901, arXiv.org.
    5. Ben-Zhang Yang & Xiaoping Lu & Guiyuan Ma & Song-Ping Zhu, 2019. "Robust portfolio optimization with multi-factor stochastic volatility," Papers 1910.06872, arXiv.org, revised Jun 2020.

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