Portfolio Credit Risk Measurement Of Baosteel, XinKe New Materials, Tiayuan Chemicai Based On Copula Function

The rapidly growing credit derivatives market, urgently need a technology, which can accurately measure the portfolio credit risk. So how to measure the correlation structure between each credit risks is the key problem of portfolio credit risks. According to China's specific situation and actual data, one new technology was used:KMV model was firstly used on the listed companies in China to estimate the probability of default. Then using the relationship between the hazard rate and the default probabilities we can obtain the distribution function of "time-until-default", and finally combined with the copula function to calculate the portfolio probability of default.In this paper, our research shows how to measure a portfolio credit risk using the copula function. And try to explain the following three points:1.KMV model suited to measure the credit risk of listed companies in China; 2.copula function can be more precisely measure of portfolio credit risk; and 3. How to select a copula function, according to the realistic data.Firstly, we use the Moody's KMV model, which mainly basis on the volatility of stock returns, stock prices, asset and liability of listed companies, to measure the single credit risk. And those indicators in China can be obtaining easily. KMV model not only involves the financial aspects of enterprise information, but also the stock information. This makes the KMV model not only reflects the information in the past, but also the prospect of the company. So comparing to others, KMV model is more suitable to measurement the credit risk of listed companies in China.Only measuring the credit risk of single listed companies can not fully reflect the true risk which commercial banks are facing. When the associated company change in credit status, there will be certainly affect on its credit risk. Practice shows appropriately using of correlation between the assets portfolio can effectively hedge their risks. Understanding the correlation between the multi-dimensional credit risks can help us get better risk management. In this paper we use the copula function approach to explore the joint distribution of credit risk.Before introducing the copula function, we first introduce a continuous random variable-the survival time. This correlation between the multi-dimensional credit risks can be defined as the related structures of their survival time. Then we discuss why using copula function to explore the joint distribution of multidimensional credit risk, and introduce the definition of copula function and its basic properties. This paper introduces five most frequently used copula function in the financial risk management:Normal-Copula, t-Copula. Gumbel-Copula, Frank-Copula and Clayton-Copula. Specific forms, features and density of the tail distribution of these five functions are introduced in detail.In portfolio credit risk measurement, the most difficult and most critical is how to select copula function. Whether or not choosing the right copula function directly affects the accuracy of credit risk measurement. Parameters of these five copula function were estimated, and the goodness of fit test-CvM test and KS test, based on the empirical copula function, were done too. Monte Carlo simulation method was using to calculate the CvM and KS values, whose approximate P-values obtained by the bootstrap method. By goodness of fit tests for copula and comparing u-Kθ(u) with u-K(u), we find that Clayton-copula can express the listed companies's related structural information better. So Clayton-copula can give a more accurate measure of portfolio credit risk. While the other four functions to some extent underestimation of portfolio credit risk.At last, portfolio credit risk of the listed companies in China in different states was measured combining Clayton-copula with the KMV model. From the joint default probability distribution, we can find that portfolio credit risk is lower than the credit risk of individual, and the interaction between the risks are more obvious, indicating that this technology can be well in portfolio credit risk management. Therefore, there is important practical significance, according to the actual conditions and historical data to identify the most appropriate copula function combining with KMV model for improving the effectiveness of portfolio credit risk management.