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Multivariate tempered stable additive subordination for financial models

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  • Patrizia Semeraro

Abstract

We study a class of multivariate tempered stable distributions and introduce the associated class of tempered stable Sato subordinators. These Sato subordinators are used to build additive inhomogeneous processes by subordination of a multiparameter Brownian motion. The resulting process is additive and time inhomogeneous. Furthermore, these processes are associated with the distribution at unit time of a class of L\'evy process with good fit properties on fifinancial data. The main feature of the Sato subordinated Brownian motion is that it has time dependent correlation, whereas the L\'evy counterpart does not. We provide a numerical illustration of the correlation dynamics.

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  • Patrizia Semeraro, 2021. "Multivariate tempered stable additive subordination for financial models," Papers 2105.00844, arXiv.org, revised Sep 2021.
    • Handle: RePEc:arx:papers:2105.00844
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    References listed on IDEAS

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    1. 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.
    2. Sato, Ken-iti, 1982. "Absolute continuity of multivariate distributions of class L," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 89-94, March.
    3. repec:dau:papers:123456789/1380 is not listed on IDEAS
    4. Patrizia Semeraro, 2020. "A note on the multivariate generalized asymmetric Laplace motion," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(10), pages 2339-2355, May.
    5. Elisa Luciano & Patrizia Semeraro, 2010. "A Generalized Normal Mean-Variance Mixture For Return Processes In Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 415-440.
    6. Petar Jevtić & Marina Marena & Patrizia Semeraro, 2019. "Multivariate Marked Poisson Processes And Market Related Multidimensional Information Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-26, March.
    7. Thomas Kokholm & Elisa Nicolato, 2010. "Sato Processes in Default Modelling," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(5), pages 377-397.
    8. Pérez-Abreu, Victor & Stelzer, Robert, 2014. "Infinitely divisible multivariate and matrix Gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 155-175.
    9. Jing Li & Lingfei Li & Rafael Mendoza-Arriaga, 2016. "Additive subordination and its applications in finance," Finance and Stochastics, Springer, vol. 20(3), pages 589-634, July.
    10. Rafael Mendoza-Arriaga & Vadim Linetsky, 2016. "Multivariate Subordination Of Markov Processes With Financial Applications," Mathematical Finance, Wiley Blackwell, vol. 26(4), pages 699-747, October.
    11. 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.
    12. Elisa Luciano & Marina Marena & Patrizia Semeraro, 2016. "Dependence calibration and portfolio fit with factor-based subordinators," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1037-1052, July.
    13. Sato, Ken-iti, 2001. "Subordination and self-decomposability," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 317-324, October.
    14. Lynn Boen & Florence Guillaume, 2019. "Building multivariate Sato models with linear dependence," Quantitative Finance, Taylor & Francis Journals, vol. 19(4), pages 619-645, April.
    15. Helyette Geman & C. Peter M. Dilip Y. Marc, 2007. "Self decomposability and option pricing," Post-Print halshs-00144193, HAL.
    16. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2007. "Self‐Decomposability And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 31-57, January.
    17. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    18. Ernst Eberlein & Dilip Madan, 2009. "Sato processes and the valuation of structured products," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 27-42.
    19. Patrizia Semeraro, 2008. "A Multivariate Variance Gamma Model For Financial Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-18.
    20. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
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