Approximation of bivariate copulas by patched bivariate Fréchet copulas

Yanting Zheng, Jingping Yang, Jianhua Z. Huang

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, independence and countermonotonicity. They are easily interpretable but have limitations when used as approximations to general dependence structures. To improve the approximation property of the BF copulas and keep the advantage of easy interpretation, we develop a new copula approximation scheme by using BF copulas locally and patching the local pieces together. Error bounds and a probabilistic interpretation of this approximation scheme are developed. The new approximation scheme is compared with several existing copula approximations, including shuffle of min, checkmin, checkerboard and Bernstein approximations and exhibits better performance, especially in characterizing the local dependence. The utility of the new approximation scheme in insurance and finance is illustrated in the computation of the rainbow option prices and stop-loss premiums. © 2010 Elsevier B.V.
Original languageEnglish (US)
Pages (from-to)246-256
Number of pages11
JournalInsurance: Mathematics and Economics
Issue number2
StatePublished - Mar 2011
Externally publishedYes


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