Approximation of bivariate copulas by patched bivariate Fréchet copulas

Zheng, Yanting; Yang, Jingping; Huang, Jianhua Z.

Approximation of bivariate copulas by patched bivariate Fréchet copulas

Type

Article

Authors

Zheng, Yanting
Yang, Jingping
Huang, Jianhua Z.

KAUST Grant Number

KUS-C1-016-04

Date

2011-03

Abstract

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.

Citation

Zheng Y, Yang J, Huang JZ (2011) Approximation of bivariate copulas by patched bivariate Fréchet copulas. Insurance: Mathematics and Economics 48: 246–256. Available: http://dx.doi.org/10.1016/j.insmatheco.2010.11.002.

Acknowledgements

We thank the reviewer for his helpful comments. Yang's research was partly supported by the National Basic Research Program (973 Program) of China (2007CB814905) and the National Natural Science Foundation of China (Grants No. 10871008). Yang also thanks National Science Foundation (DMS-0630950) of the US for supporting his visit to Texas A&M University through the Virtual Center for Collaboration between Statisticians in the US and China, where some initial ideas of the project was developed. Huang's research was partly supported by the National Cancer Institute (CA57030) and the National Science Foundation (DMS-0907170) of the US, and by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).