Tail Dependence, Tail Asymmetry and Credit Portfolio Risk

Abstract

In the risk management of the credit portfolio of a bank, Normal copula is standard for modelling dependencies between each credit in the portfolio. The Normal copula modelling is criticized by the tendency of underestimation of the risk due to its asymptotic independence. This paper analyses the effect of dependence between each extreme value movement in the credit portfolio. First, the relation between the extreme tail dependence or tail asymmetry and the joint default probability is summarized by referring to preceding works on bivariate extreme value. Second, the risk valuation of the credit portfolio and the pricing of CLO tranche are done by simulation where the credit portfolio and the CLO pool consists of 1,000 firms' credit. The simulation results imply the effect of extreme or tail dependence and tail asymmetry in the credit portfolio risk or CLO tranche value through the strength of the joint default probabilities of each pair in the portfolio.