TY - JOUR
T1 - The t copula with multiple parameters of degrees of freedom
T2 - bivariate characteristics and application to risk management
AU - Luo, Xiaolin
AU - Shevchenko, Pavel V.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77958575218&partnerID=8YFLogxK
U2 - 10.1080/14697680903085544
DO - 10.1080/14697680903085544
M3 - Article
AN - SCOPUS:77958575218
VL - 10
SP - 1039
EP - 1054
JO - Quantitative Finance
JF - Quantitative Finance
SN - 1469-7688
IS - 9
ER -