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arXiv · 0710.3959

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

Xiaolin Luo·Pavel V. Shevchenko
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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.

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Xiaolin Luo, Pavel V. Shevchenko. 2010-02-16. The t copula with Multiple Parameters of Degrees of Freedom: Bivariate Characteristics and Application to Risk Management. https://doi.org/10.1080/14697680903085544

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