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Copulas in finance and insurance

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  • Rosario Romera

    ()

  • Elisa M. Molanes

    ()

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    Abstract

    Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing.

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    Bibliographic Info

    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws086321.

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    Date of creation: Nov 2008
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    Handle: RePEc:cte:wsrepe:ws086321

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    Related research

    Keywords: Dependence structure; Extremal values; Copula modeling; Copula review;

    References

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    1. Yu, Lining & Voit, Eberhard O., 2006. "Construction of bivariate S-distributions with copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1822-1839, December.
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    3. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
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    13. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    14. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    15. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    16. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650.
    17. Belzunce, Felix & Ortega, Eva-Maria & Pellerey, Franco & Ruiz, Jose M., 2006. "Variability of total claim amounts under dependence between claims severity and number of events," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 460-468, June.
    18. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
    19. Yang, Jingping & Cheng, Shihong & Zhang, Lihong, 2006. "Bivariate copula decomposition in terms of comonotonicity, countermonotonicity and independence," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 267-284, October.
    20. Rosenberg, Joshua V. & Schuermann, Til, 2006. "A general approach to integrated risk management with skewed, fat-tailed risks," Journal of Financial Economics, Elsevier, vol. 79(3), pages 569-614, March.
    21. A. Sancetta & Satchell, S.E., 2001. "Bernstein Approximations to the Copula Function and Portfolio Optimization," Cambridge Working Papers in Economics 0105, Faculty of Economics, University of Cambridge.
    22. Kaishev, Vladimir K. & Dimitrova, Dimitrina S. & Haberman, Steven, 2007. "Modelling the joint distribution of competing risks survival times using copula functions," Insurance: Mathematics and Economics, Elsevier, vol. 41(3), pages 339-361, November.
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