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Bernstein Approximations to the Copula Function and Portfolio Optimization

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  • A. Sancetta
  • Satchell, S.E.

Abstract

The copula function is considered within the context of financial multivariate data sets that are not normally distributed. The Bernstein polynomial approximation to copulae is given and motivated by its desirable properties. The multivariate convergence properties are analysed. The concept of Bernstein copula is introduced as a generalisation of some bivariate and higher dimensional families of copulae. Statistical properties of the Bernstein copula are studied together with implementation issues related to portfolio theory and expected utility optimisation.

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File URL: http://www.econ.cam.ac.uk/dae/repec/cam/pdf/wp0105.pdf
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Bibliographic Info

Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0105.

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Length: 47
Date of creation: Jun 2001
Date of revision:
Handle: RePEc:cam:camdae:0105

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Keywords: copulae; Bernstein polynomials; approximation theory; portfolio;

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References

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  1. James Tobin, 1956. "Liquidity Preference as Behavior Towards Risk," Cowles Foundation Discussion Papers 14, Cowles Foundation for Research in Economics, Yale University.
  2. Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor and Francis Journals, vol. 18(3), pages 287-330.
  3. Hagerman, Robert L, 1978. "More Evidence on the Distribution of Security Returns," Journal of Finance, American Finance Association, vol. 33(4), pages 1213-21, September.
  4. Peter C.B. Phillips, 1982. "ERA's: A New Approach to Small Sample Theory," Cowles Foundation Discussion Papers 645, Cowles Foundation for Research in Economics, Yale University.
  5. Nelsen, Roger B., 1997. "Dependence and Order in Families of Archimedean Copulas," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 111-122, January.
  6. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
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Citations

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Cited by:
  1. Alessio Sancetta, 2004. "Copula Based Monte Carlo Integration in Financial Problems," Working Papers wp04-02, Warwick Business School, Financial Econometrics Research Centre.
  2. Szego, Giorgio, 2002. "Measures of risk," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1253-1272, July.
  3. Fortin, Ines & Kuzmics, Christoph, 2002. "Tail-Dependence in Stock-Return Pairs," Economics Series 126, Institute for Advanced Studies.
  4. Rosario Romera & Elisa M. Molanes, 2008. "Copulas in finance and insurance," Statistics and Econometrics Working Papers ws086321, Universidad Carlos III, Departamento de Estadística y Econometría.

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