The t copula with Multiple Parameters of Degrees of Freedom: Bivariate Characteristics and Application to Risk Management

TL;DR

This paper introduces a novel grouped t copula with individual degrees of freedom for each risk, enhancing modeling flexibility for tail dependence in risk management applications.

Contribution

It proposes a grouped t copula where each risk has its own dof, removing the need for a priori grouping and improving tail dependence modeling.

Findings

The new copula differs significantly from the standard t copula in risk measures.

Simulation and calibration procedures are developed and tested.

Finite sample properties of estimators are analyzed.

Abstract

The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case. To overcome this problem, grouped t copula was proposed recently, where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter. In this paper we propose the use of a grouped t copula, where each group consists of one risk factor only, so that a priori grouping is not required. The copula characteristics in the bivariate case are studied. We explain simulation and calibration procedures, including a simulation study on finite sample properties of the maximum likelihood estimators and Kendall's tau approximation. This new copula can be significantly different from the standard t copula in terms of risk measures such as tail dependence, value at risk and expected shortfall. Keywords: grouped t copula, tail dependence, risk management.