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 new t copula, generalizing grouped t copula to have each group consisting of one risk  only, so that a priori grouping is not required. The characteristics of this copula in the bivariate case are described . We explain simulation and calibration procedures and provide examples .
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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new t copula, generalizing
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to have each group consisting
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characteristics of this copula
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described
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and provide examples
, 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