Credit Risk Measurement Basing On The Modified CreditRisk+ Model

Credit risk plays a significant role in the commercial banks and other finance departments. Quantifying the Credit Risk can make the relationship of the credit risk, interest rate risk, fluidity risk and other risks. What's more, it make us know better about the mutual influence between the single risk, the assembled risks and the entire risks of the banks, which makes it more efficient to manage the risk and avoid the unexpected losses. However, the technique of measuring the Credit Risk developed lately in China and the classification of the Credit is immature as the foreign countries. As a result, some of the techniques, such as the KMV model, the Credit Metrics model and the Credit Portfolio model, that develop well in other countries can not be used in China directly because of the limited conditions. Compared with other models, the CreditRisk+ model is a relative simple but useful Credit Risk model. This model focuses on the analysis of the default and just has to estimate several variables, such as the probability of the default, the rate of the default losses and the risk exposure. This model can deal with thousands of risk exposures of different areas, different departments and different terms. The most significant advantage of this model is that it just requires little data and as a result can make up the fact that the data in Chinese banks is limited, which is attractive and facilitate the implementation of the model.There are several problems when the Panjer arithmetic is used to calculate the Credit Risk VaR. For example, when theμ. is large enough, the computer will recognize the e^-μ as 0, as a result, the arithmetic will stop. Meantime, this arithmetic divide the risk exposures into different bands and approximate those risk exposures as integers, which influence the accuracy of the results and the accumulated errors will lead bigger error. Michael B. Gordy pointed out that the saddle point approximation can solve the problem in 2002. The most advantage of the saddle point approximation is that it performed exactly well on the tail approximation, which solves the problem of the heavy tails, one of the most significant problems that the banks concern, of the risk distribution. Meanwhile, the Saddle point approximation has more advantages than the Panjer arithmetic. It dose not have to divide the risk exposures into different bands; it uses the value of the default directly in the calculation, which make it more accurate and steady and avoid the error of the approximation. The saddle point approximation is more quickly and more simple in the calculation and can avoid the Monte carlo simulation.In Michael B. Gordy's model, he assumes the rate of the default losses is a fixed value. However, in the actual financial market, the rate of the default losses can be influenced by the priority of the reclaim, the department, the cycle of the economics and the condition of the macroeconomic. As a result, the rate of the default losses is a random variable, rather than a fixed value. This article recognizes the rate of the default losses as a normal distribution and deduces the expression of the Credit risk VaR. Furthermore, this article carries a series of simulation by using the Matlab. The simulation results reveals that the value of credit risk VaR is higher when the rate of the default losses is considered as a normal distribution. The biggest difference in the simulation of this article can be 10.72%.The method used to calculate the Credit risk in this article is different from the one used in Michael B. Gordy's article. In Michael B. Gordy's article, he formed a fine grid of z^* values in an open interval and calculate the corresponding y, w and u from the derivatives ofψat each point in the grid, then he form a table of pairs(1-G(y),y) by using the Lugannani-Rice formula and interpolate to find the valueof y corresponding to 1-G(y)=1-q. This article adopt a formula to approximate the value of the CDF of the standard normal distribution, which just have a maximumerror of 7.5×10^-8. By doing this, it is practicable and convenient to calculate theCredit risk VaR. Also, by using the function in the Matlab, it is much easier to calculate the zero value and can avoid the process of forming a fine grid. This method is more quickly, more convenient and can avoid the accumulated errors in the calculation, which makes it more accurate in the calculation. At last, this article points out that we can do further research on the condition that the Macor-economic factors have the stochastic fluctuation variance, instead of the constant one.