The t copula with multiple parameters of degrees of freedom: bivariate characteristics and application to risk management

Xiaolin Luo*, Pavel V. Shevchenko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)

Abstract

The t copula is often used in risk management as it allows for modeling the 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, the 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 generalized 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 the finite sample properties of the maximum likelihood estimators and Kendall's tau approximation. This new copula is significantly different from the standard t copula in terms of risk measures such as tail dependence, value at risk and expected shortfall.

Original languageEnglish
Pages (from-to)1039-1054
Number of pages16
JournalQuantitative Finance
Volume10
Issue number9
DOIs
Publication statusPublished - 2010
Externally publishedYes

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