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Exact Simulation of the Wishart Multidimensional Stochastic Volatility Model

Author

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  • Chulmin Kang

    (KTB Investment and Securities, Seoul 07325, Republic of Korea)

  • Wanmo Kang

    (Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea)

  • Jong Mun Lee

    (MERITZ Fire and Marine Insurance, Seoul 06232, Republic of Korea)

Abstract

In this article, we propose an exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model—a single asset model with a multidimensional Wishart variance process. Our method is based on analysis of the conditional characteristic function of the log-price given a terminal volatility level. In particular, we found an explicit expression for the conditional characteristic function for the Heston model. Numerical experiments demonstrate that our new method is much faster and reliable than the Euler discretization method.

Suggested Citation

  • Chulmin Kang & Wanmo Kang & Jong Mun Lee, 2017. "Exact Simulation of the Wishart Multidimensional Stochastic Volatility Model," Operations Research, INFORMS, vol. 65(5), pages 1190-1206, October.
    • Handle: RePEc:inm:oropre:v:65:y:2017:i:5:p:1190-1206
    DOI: 10.1287/opre.2017.1636
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    References listed on IDEAS

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    Cited by:

    1. Pingping Zeng & Ziqing Xu & Pingping Jiang & Yue Kuen Kwok, 2023. "Analytical solvability and exact simulation in models with affine stochastic volatility and Lévy jumps," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 842-890, July.
    2. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2023. "Shot-noise cojumps: exact simulation and option pricing," LSE Research Online Documents on Economics 111537, London School of Economics and Political Science, LSE Library.
    3. Jaehyuk Choi, 2024. "Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Lo\`eve expansions," Papers 2402.09243, arXiv.org.
    4. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    5. Li, Chenxu & Wu, Linjia, 2019. "Exact simulation of the Ornstein–Uhlenbeck driven stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 275(2), pages 768-779.
    6. Jaehyuk Choi & Yue Kuen Kwok, 2023. "Simulation schemes for the Heston model with Poisson conditioning," Papers 2301.02800, arXiv.org, revised Nov 2023.

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