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On the Use of Copulas for Calculating the Present Value of a General Cash Flow


  • M. Goovaerts
  • A. De Schepper
  • Y. Hua
  • G. Darkiewicz
  • D: Vyncke


In a paper of 2000, Kaas, Dhaene and Goovaerts investigate the present value of a rather general cash flow as a special case of sums of dependent risks. Making use of comonotonic risks, they derive upper and lower bounds for the distribution of the present value, in the sense of convex ordering. These bounds are very close to the real distribution in case all payments have the same sign; however, if there are both positive and negative payments, the upper bounds perform rather badly. In the present contribution we show what happens when solving this problem by means of copulas. The idea consists of splitting up the total present value in the difference of two present values with positive payments. Making use of a copula as an approximation for the joint distribution of the two sums, an approximation for the distribution of the original present value can be derived.

Suggested Citation

  • M. Goovaerts & A. De Schepper & Y. Hua & G. Darkiewicz & D: Vyncke, 2005. "On the Use of Copulas for Calculating the Present Value of a General Cash Flow," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business, Review of Business and Economic Literature, vol. 0(1), pages 69-94.
  • Handle: RePEc:ete:revbec:20050107

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    References listed on IDEAS

    1. Bovenberg, A. Lans & Graafland, Johan J. & de Mooij, Ruud A., 2000. "Tax reform and the Dutch labor market: an applied general equilibrium approach," Journal of Public Economics, Elsevier, vol. 78(1-2), pages 193-214, October.
    2. Donders, Jan & Graafland, Johan, 1998. "CPB models and employment policy in the Netherlands," Economic Modelling, Elsevier, vol. 15(3), pages 341-356, July.
    3. Graafland, J.J. & Huizinga, F.H., 1998. "Taxes and benefits in a non-linear wage equation," MPRA Paper 21076, University Library of Munich, Germany.
    4. Draper, D.A.G., 2000. "Towards an econometric model for the Netherlands : Explaining unemployment," Other publications TiSEM 8d6f0572-d552-4ca2-9df3-6, Tilburg University, School of Economics and Management.
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