Joint Commercial Bank Credit Risk And Interest Rate Risk Measure Study

Following Merton (1974), thousands of theoretic and empirical literatures have been exploring how to measure credit risk with changes in asset value. However, the joint measurement of credit and interest rate risk based on the correlation between asset values and risk-free rates is just a new topic.As a risk-taking financial institution, the commercial bank takes credit risk as its primary concern. With the deepening of interest rate liberalization in China, Chinese commercial banks face the new challenge of interest rate risk, which is intrinsically negatively related to credit risk. This paper identifies the difference between the other two types of correlation, which are correlation between credit spreads and risk-free rates and correlation between market index and risk-free rates. The difficulty here is that market index is usually treated as the intermediate proxy of credit spread, which misleads people to take it for granted that the above two correlations are virtually equal. This paper, however, finds that there are two opposing transmission channels for correlation between market index and risk-free rates.Joint modeling in this paper is developed by the introduction of stochastic interest rates to the structural approach and reduced-form approach, which are the two main approaches for measuring credit risk. The paper consists of theoretic and simulation analysis. The theoretic joint measurement models derive the correlation between spot rate, market index and industry indexes both for the structural approach and for the reduced-form approach. The Monte Calo simulation method generates simulated credit ratings migration metrics and term structure, which are then used to calculate the joint VaRs of individual loans and loan portfolios. Moreover, sensitivity analysis is made by stress testing on the parameters of initial credit ratings, correlation coefficients, probability of default and loss given default. Modeling the credit process by simulating market index and industry index movement, the paper achieves three advantages. First, it accurately reflects the idea of structural approach, whose basic assumption is that changes in a firm's credit quality are the result of changes in its asset value. Second, the correlation structure in a credit portfolio is estimated by the empirical correlation coefficients between industry indexes and risk-free rate. Third, simulated migration metrics are generated to serve the purpose of stress testing in banks' daily risk management.The paper comes to two theoretic conclusions. First, the negative correlationbetween risk-free rate and credit spread is not a mere superficial phenomenon, but is driven by economic forces. In the risk neutral pricing framework, risk-free rate is the drift term (mean) of movement in asset value. Second, it is important to group debt by industries when modeling correlated credit and interest rate risk, since different industries have different sensitivity coefficients to various macroeconomic variables. Empirical evidence tells us that credit spreads of bonds with the same credit rating may differ greatly if they differ in industries. We find that the credit spread differences in industry are the result of different correlation coefficients between interest rates and various industries, which are further caused by differed sensitivity of industries to the business cycle and the consequent up and down movements in interest rates.The simulation results in this paper have two findings from the perspective of correlated modeling. First, 20 loans from different industries make a widely diversified portfolio, increasing the number of loans does not achieve better diversification effect. The joint VaR is less than the sum of credit VaR and interest rate VaR, due to the negative correlation between credit and interest rate risk. Second, the credit portfolio is sensitive to the parameters such as the correlation between credit and interest rate risk, default correlation and initial credit ratings, while individual loans are more sensitive to the probability of default, loss given default and also initial ratings. The weight of interest rate risk is higher for an investment grade obligor, while credit risk dominates the risk of a non-investment obligor.Finally, it is important to note that besides our main objects of fixed-rate loans and bonds, we extend the research into risk measurement of floating-rate loans and retail credit. Illiquidity discount and internal credit ratings are also studied. The same methodology of joint modeling can be applied to risk management of financial derivatives. All of these can help commercial banks and regulators calculate the joint VaRs more precisely, which is the practical value of this paper.