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A Multivariate Time-Changed Lévy Model for Financial Applications

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  • Patrizia Semeraro

Abstract

The purpose of this paper is to define a bivariate L´evy process by subordination of a Brownian motion. In particular we investigate a generalization of the bivariate Variance Gamma process proposed in Luciano and Schoutens [8] as a price process. Our main contribution here is to introduce a bivariate subordinator with correlated Gamma margins. We characterize the process and study its dependence structure. At the end wealso propose an exponential Lévy price model based on our process.

Suggested Citation

  • Patrizia Semeraro, 2006. "A Multivariate Time-Changed Lévy Model for Financial Applications," ICER Working Papers - Applied Mathematics Series 10-2006, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:10-2006
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    File URL: http://www.bemservizi.unito.it/repec/icr/wp2006/ICERwp10-06.pdf
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    References listed on IDEAS

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    1. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
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    Cited by:

    1. Boris Buchmann & Benjamin Kaehler & Ross Maller & Alexander Szimayer, 2015. "Multivariate Subordination using Generalised Gamma Convolutions with Applications to V.G. Processes and Option Pricing," Papers 1502.03901, arXiv.org, revised Oct 2016.
    2. 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.
    3. 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.
    4. Asmerilda Hitaj & Lorenzo Mercuri, 2013. "Portfolio allocation using multivariate variance gamma models," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 27(1), pages 65-99, March.
    5. Marina Marena & Andrea Romeo & Patrizia Semeraro, 2018. "Multivariate Factor-Based Processes With Sato Margins," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-30, February.
    6. Roman Ivanov, 2015. "The distribution of the maximum of a variance gamma process and path-dependent option pricing," Finance and Stochastics, Springer, vol. 19(4), pages 979-993, October.
    7. Marina Marena & Andrea Romeo & Patrizia Semeraro, 2015. "Pricing multivariate barrier reverse convertibles with factor-based subordinators," Carlo Alberto Notebooks 439, Collegio Carlo Alberto.
    8. Petar Jevtic & Patrizia Semeraro, 2014. "A class of multivariate marked Poisson processes to model asset returns," Carlo Alberto Notebooks 351, Collegio Carlo Alberto.
    9. Elisa Luciano & Patrizia Semeraro, 2007. "Generalized Normal Mean Variance Mixture and Subordinated Brownian Motion," ICER Working Papers - Applied Mathematics Series 42-2007, ICER - International Centre for Economic Research.
    10. Asmerilda Hitaj & Friedrich Hubalek & Lorenzo Mercuri & Edit Rroji, 2016. "Multivariate Mixed Tempered Stable Distribution," Papers 1609.00926, arXiv.org, revised Oct 2016.
    11. Ivanov Roman V., 2018. "On risk measuring in the variance-gamma model," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 23-33, January.
    12. Florence Guillaume, 2018. "Multivariate Option Pricing Models With Lévy And Sato Vg Marginal Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-26, March.
    13. Florence Guillaume, 2013. "The αVG model for multivariate asset pricing: calibration and extension," Review of Derivatives Research, Springer, vol. 16(1), pages 25-52, April.
    14. Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2018. "Calibration for Weak Variance-Alpha-Gamma Processes," Papers 1801.08852, arXiv.org, revised Jul 2018.
    15. Alexandre Petkovic, 2009. "Three essays on exotic option pricing, multivariate Lévy processes and linear aggregation of panel models," ULB Institutional Repository 2013/210357, ULB -- Universite Libre de Bruxelles.
    16. Karl Friedrich Hofmann & Thorsten Schulz, 2016. "A General Ornstein–Uhlenbeck Stochastic Volatility Model With Lévy Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-23, December.

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