New Families of Copulas Based on Periodic Functions

Abstract

Although there exists a large variety of copula functions, only a few are practically manageable, and often the choice in dependence modeling falls on the Gaussian copula. Further, most copulas are exchangeable, thus implying symmetric dependence. We introduce a way to construct copulas based on periodic functions. We study the two-dimensional case based on one dependence parameter and then provide a way to extend the construction to the n-dimensional framework. We can thus construct families of copulas in dimension n and parameterized by n − 1 parameters, implying possibly asymmetric relations. Such "periodic" copulas can be simulated easily.

Construction of asymmetric multivariate copulas

“…Suitable families of copulas are also needed for parametric and semiparametric estimation methods for multivariate densities and distribution functions. Alfonsi and Brigo [1] describe a new construction method for asymmetric copulas based on periodic functions. A transformation E-mail address: eckhard.liebscher@hs-merseburg.de.…”

A new family of symmetric bivariate copulas

“…'s and, moreover, it is precisely the copula that captures the dependence properties. Several families of copulas are collected, for example, in [4], and many others have been introduced recently (see, e.g., [1,2,6]). Here, we present a family of (bivariate) copulas, which includes many other families, such as the well-known Cuadras-Augé [3], we study its properties in details and provide several examples.…”

The distribution of realized variances: Marginal behaviors, asymmetric dependence and contagion effects

“…Asymmetric copula models are very new and the literature is reduced. Alfonsi and Brigo (2005) introduce a construction method for these models based on periodic functions. In this article we rely on another method for developing asymmetric copulas connected with the product of copulas that is proposed in a special case by Khoudraji (1995) and generalized in Liebscher (2008).…”