Approximation of bivariate copulas by patched bivariate Fréchet copulas

Handle URI:
http://hdl.handle.net/10754/597602
Title:
Approximation of bivariate copulas by patched bivariate Fréchet copulas
Authors:
Zheng, Yanting; Yang, Jingping; Huang, Jianhua Z.
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.
Publisher:
Elsevier BV
Journal:
Insurance: Mathematics and Economics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Mar-2011
DOI:
10.1016/j.insmatheco.2010.11.002
Type:
Article
ISSN:
0167-6687
Sponsors:
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).
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Full metadata record

DC FieldValue Language
dc.contributor.authorZheng, Yantingen
dc.contributor.authorYang, Jingpingen
dc.contributor.authorHuang, Jianhua Z.en
dc.date.accessioned2016-02-25T12:42:52Zen
dc.date.available2016-02-25T12:42:52Zen
dc.date.issued2011-03en
dc.identifier.citationZheng 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.en
dc.identifier.issn0167-6687en
dc.identifier.doi10.1016/j.insmatheco.2010.11.002en
dc.identifier.urihttp://hdl.handle.net/10754/597602en
dc.description.abstractBivariate 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.en
dc.description.sponsorshipWe 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).en
dc.publisherElsevier BVen
dc.subjectApproximation of bivariate copulasen
dc.subjectBivariate Fréchet copulasen
dc.subjectPatched bivariate Fréchet copulaen
dc.subjectRainbow optionsen
dc.titleApproximation of bivariate copulas by patched bivariate Fréchet copulasen
dc.typeArticleen
dc.identifier.journalInsurance: Mathematics and Economicsen
dc.contributor.institutionPeking University, Beijing, Chinaen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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