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Computation of copulas by Fourier methods

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  • Antonis Papapantoleon

Abstract

We provide an integral representation for the (implied) copulas of dependent random variables in terms of their moment generating functions. The proof uses ideas from Fourier methods for option pricing. This representation can be used for a large class of models from mathematical finance, including L\'evy and affine processes. As an application, we compute the implied copula of the NIG L\'evy process which exhibits notable time-dependence.

Suggested Citation

  • Antonis Papapantoleon, 2011. "Computation of copulas by Fourier methods," Papers 1108.1216, arXiv.org, revised Jun 2014.
    • Handle: RePEc:arx:papers:1108.1216
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    1. Kallsen, Jan & Tankov, Peter, 2006. "Characterization of dependence of multidimensional Lévy processes using Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1551-1572, August.
    2. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    3. Elisa Luciano & Wim Schoutens, 2006. "A multivariate jump-driven financial asset model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 385-402.
    4. 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.
    5. Reiichiro Kawai, 2009. "A multivariate Levy process model with linear correlation," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 597-606.
    6. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2010. "Analysis of Fourier Transform Valuation Formulas and Applications," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 211-240.
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