New copulas based on general partitions-of-unity (part III) - the continuous case (extended version)

TL;DR

This paper introduces a method to extend discrete partition-of-unity copulas to continuous ones, enabling better modeling of tail dependence in high-dimensional data for risk management applications.

Contribution

It presents a simple algorithm for generating continuous copulas from empirical data, incorporating positive tail dependence for improved risk modeling.

Findings

Allows for continuous copula construction from high-dimensional data

Enables implementation of positive tail dependence

Applicable to risk management and Solvency II models

Abstract

In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields. We present a general simple algorithm to generate such copulas on the basis of the empirical copula from high-dimensional data sets. In particular, our constructions also allow for an implementation of positive tail dependence which sometimes is a desirable property of copula modelling, in particular for internal models under Solvency II.