A new bivariate extension of FGM copulas
C\'ecile Amblard, St\'ephane Girard
TL;DR
This paper introduces a new family of bivariate copulas extending the FGM family, capable of modeling high positive dependence with flexible Spearman's Rho and tail dependence, supported by theoretical conditions and examples.
Contribution
It presents a novel copula family generated by two functions, expanding the dependence modeling capabilities beyond traditional FGM copulas.
Findings
Range of Spearman's Rho is [-3/4, 1]
Upper tail dependence coefficient can reach any value in [0, 1]
Provides conditions for dependence properties
Abstract
We propose a new family of copulas generalizing the Farlie-Gumbel-Morgenstern family and generated by two univariate functions. The main feature of this family is to permit the modeling of high positive dependence. In particular, it is established that the range of the Spearman's Rho is [-3/4,1] and that the upper tail dependence coefficient can reach any value in [0,1]. Necessary and sufficient conditions are given on the generating functions in order to obtain various dependence properties. Some examples of parametric subfamilies are provided.
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Insurance, Mortality, Demography, Risk Management · Probability and Risk Models