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The multivariate Variance Gamma model: basket option pricing and calibration

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  • Daniël Linders
  • Ben Stassen

Abstract

In this paper, we propose a methodology for pricing basket options in the multivariate Variance Gamma model introduced in Luciano and Schoutens [ Quant. Finance 6 (5), 385--402]. The stock prices composing the basket are modelled by time-changed geometric Brownian motions with a common Gamma subordinator. Using the additivity property of comonotonic stop-loss premiums together with Gauss-Laguerre polynomials, we express the basket option price as a linear combination of Black & Scholes prices. Furthermore, our new basket option pricing formula enables us to calibrate the multivariate VG model in a fast way. As an illustration, we show that even in the constrained situation where the pairwise correlations between the Brownian motions are assumed to be equal, the multivariate VG model can closely match the observed Dow Jones index options.

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  • Daniël Linders & Ben Stassen, 2016. "The multivariate Variance Gamma model: basket option pricing and calibration," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 555-572, April.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:4:p:555-572
    DOI: 10.1080/14697688.2015.1043934
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    Citations

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    Cited by:

    1. Roman V. Ivanov, 2018. "A Credit-Risk Valuation under the Variance-Gamma Asset Return," Risks, MDPI, vol. 6(2), pages 1-25, May.
    2. Rafał Wójcik & Charlie Wusuo Liu, 2022. "Bivariate Copula Trees for Gross Loss Aggregation with Positively Dependent Risks," Risks, MDPI, vol. 10(8), pages 1-24, July.
    3. Luca De Gennaro Aquino & Carole Bernard, 2019. "Bounds on Multi-asset Derivatives via Neural Networks," Papers 1911.05523, arXiv.org, revised Nov 2020.
    4. Pier Francesco Procacci & Tomaso Aste, 2018. "Forecasting market states," Papers 1807.05836, arXiv.org, revised May 2019.
    5. 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.
    6. Amit K. Sinha, 2021. "The reliability of geometric Brownian motion forecasts of S&P500 index values," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1444-1462, December.
    7. Yunfei Xia & Michael Grabchak, 2024. "Pricing multi-asset options with tempered stable distributions," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-24, December.
    8. Afhami, Bahareh & Rezapour, Mohsen & Madadi, Mohsen & Maroufy, Vahed, 2023. "A comonotonic approximation to optimal terminal wealth under a multivariate Merton model with correlated jump risk," Applied Mathematics and Computation, Elsevier, vol. 444(C).

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