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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.
    2. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(4), pages 589-607, December.
    5. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
    8. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    Cited by:

    1. 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.
    2. 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.
    3. Leonardo Perotti & Lech A. Grzelak, 2021. "Fast Sampling from Time-Integrated Bridges using Deep Learning," Papers 2111.13901, arXiv.org.
    4. 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.
    5. 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.

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