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Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing

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  • Buchmann, Boris
  • Kaehler, Benjamin
  • Maller, Ross
  • Szimayer, Alexander

Abstract

We unify and extend a number of approaches related to constructing multivariate Madan–Seneta Variance-Gamma models for option pricing. Complementing Grigelionis’ (2007) class, an overarching model is derived by subordinating multivariate Brownian motion to a subordinator from Thorin’s (1977) [58, 59] class of generalised Gamma convolutions. Multivariate classes developed by Pérez-Abreu and Stelzer (2014), Semeraro (2008) and Guillaume (2013) are submodels. The classes are shown to be invariant under Esscher transforms, and quite explicit expressions for canonical measures are obtained, which permit applications such as option pricing using PIDEs or tree based methodologies. We illustrate with best-of and worst-of European and American options on two assets.

Suggested Citation

  • Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:7:p:2208-2242
    DOI: 10.1016/j.spa.2016.10.008
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    References listed on IDEAS

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    Cited by:

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    2. Robin Merkle & Andrea Barth, 2022. "On Some Distributional Properties of Subordinated Gaussian Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2661-2688, December.
    3. M. Gardini & P. Sabino & E. Sasso, 2021. "The Variance Gamma++ Process and Applications to Energy Markets," Papers 2106.15452, arXiv.org.
    4. Matteo Gardini & Piergiacomo Sabino, 2022. "Exchange option pricing under variance gamma-like models," Papers 2207.00453, arXiv.org.
    5. Kevin W. Lu, 2022. "Calibration for multivariate Lévy-driven Ornstein-Uhlenbeck processes with applications to weak subordination," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 365-396, July.
    6. Roman V. Ivanov, 2018. "Option Pricing In The Variance-Gamma Model Under The Drift Jump," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-19, June.
    7. Buchmann, Boris & Lu, Kevin W. & Madan, Dilip B., 2020. "Self-decomposability of weak variance generalised gamma convolutions," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 630-655.
    8. Matteo Gardini & Piergiacomo Sabino & Emanuela Sasso, 2020. "Correlating L\'evy processes with Self-Decomposability: Applications to Energy Markets," Papers 2004.04048, arXiv.org, revised Jul 2020.

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