Constructing Copulas with Given Diagonal and Opposite Diagonal Sections

Abstract

A method for constructing copulas with given diagonal and opposite diagonal sections is presented. It makes use of a recently developed method for constructing cross-copulas with given horizontal and vertical sections. Conditions guaranteeing the existence of a cross-copula with the given diagonal and opposite diagonal sections are derived. It is shown how the new method facilitates the construction of families of copulas that simultaneously model tail dependences of upper-upper, upper-lower, lower-lower and lower-upper type.

Keywords:

• Copula
• Cross-copula
• Diagonal section
• Lipschitz conditions
• Opposite diagonal section
• Tail dependence

Mathematics Subject Classification:

• Primary 60E05
• Secondary 62H05
• 62E10

Acknowledgments

The third author acknowledges the support of the Ministerio de Educación y Ciencia (Spain) and FEDER, under research project MTM2006-12218.