Copula 함수를 이용한 신용포트폴리오의 dependence 구조 분석과 부도상관관계에 관한 실증 연구

Abstract

Recently, the credit portfolio market has grown rapidly both in volume and in breadth of the instruments. Therefore, more accuracy is needed in assessing the probability of default. In risk management, it is very important to estimate probability of default, loss given default, and exposure. Especially, probability of default is very important. Because it is used for pricing, structuring, setting the provision, and capital allocating which need dependence structure between assets. While credit rating and maturity can be used to assess default probability on an individual security basis, correlation, a third variable, is needed to fully assess the risk on a portfolio basis. Default correlation is an estimation for dependence structure of credit portfolio. Modeling joint defaults is a very important step. However, modeling dependent defaults is difficult because there are very few historical data available on joint defaults. An accurate assessment of correlation is important in assessing risks in portfolio basis. Copula functions are alternative ways to determine the dependence structure of assets in a portfolio. Copulas are flexible instruments used to build efficient algorithms for a better simulation of joint distribution. This paper presented the definition and some basic properties of copula functions, methodologies for estimation, and simulation for joint default and default correlation for credit portfolio. Also, the statistical procedures used to calibrate a copula function to real market data are described. The procedures are applied to a portfolio of Korean bond and its equity data. It is shown that how one can generate simulations in bivariate case using Student's t-copula function which is more appropriate model than Gaussian one.