Credit rating is an evaluation of the ability and credibility of economic entities and various financial instruments to repay principal and interest as promised. In China, there are currently five rating agencies rating corporate bonds and nearly 40 rating agencies rating the credit of loan enterprises. The rating results show that most corporate bonds are AAA and AA; The credit rating of loan enterprises is mostly normal distribution. Judging from their own evaluation results, all rating agencies will consider themselves objective. But for market users and regulatory authorities, how to determine that this AAA is equivalent to that AAA, and this AAA must be better than that AAA? How to compare and evaluate the rating results of different rating agencies on the same rating object? Then there needs to be another objective measure to test and compare the rating results-default rate.

Default rate refers to the actual default rate of the debtor's failure to repay the debts due.

The probability of default (PD) is the possibility that the debtor is expected to be unable to repay the due debt (default). The difference between default probability (PD) and default rate is that it judges the default situation in a certain period (usually one year) in the future according to the debtor's history and actual default situation. The corresponding relationship between rating results and default rate is the most important yardstick for evaluating quality standards of evaluation institutions.

In the credit risk management of commercial banks, the probability of default refers to the possibility that borrowers will not be able to repay the principal and interest of bank loans or fulfill related obligations in a certain period of time in the future. Default probability is the basis of calculating expected loan losses, loan pricing and credit portfolio management, so how to calculate default probability accurately and effectively is very important for credit risk management of commercial banks.

Credit rating has real application value only if it has corresponding default rate and default probability, and it can be used as a tool to measure the future default possibility and credit risk of rating objects. In essence, the default rate and default probability level corresponding to credit rating truly represent the risk situation reflected by credit rating. Therefore, the credit rating without default rate statistics is incomplete and unconvincing, and only the credit risks can be sorted. However, different rating agencies may have different definitions of breach of contract, and the quality of the same level is also different. Therefore, only rating agencies with the same definition of breach of contract can compare their rating results and test the "gold content" and quality difference of their rating results. By comparing the default rate indicators, we can explain why AA with low default rate is better than AAA with high default rate. With the credit rating corresponding to the default rate, it can really become the basis for decision-making.

The role of default probability measurement

For the credit risk management of commercial banks, the measurement of default probability occupies a basic position and plays an important role.

First of all, this is the first condition of credit risk management. As a basic method to measure credit risk, credit rating plays a role based on the measurement of the borrower's default probability. Only by scientifically calculating the default probability of borrowers can banks accurately calculate the expected losses, objectively and accurately evaluate the credit status of customers, and then ensure the scientific and effective credit risk management of commercial banks.

Secondly, this is an objective standard to measure the advantages and disadvantages of different rating systems. If there is no measure of default probability, it is difficult to measure the advantages and disadvantages of different rating systems; If we avoid the rigorous and scientific measurement of default probability and only pursue the construction of rating index system and the improvement of rating method, we can't realize the modernization leap of credit rating. The measurement of default probability is the soul of the authority and operability of credit rating, and it is an objective standard to measure the advantages and disadvantages of different rating systems.

Third, this is an important driving force to improve the quality of risk management of commercial banks. Practical experience shows that the successful measurement of customer default probability depends not only on the scientific application of advanced statistical models and risk quantification tools, but also on the in-depth understanding and scientific grasp of modern commercial bank management rules, which need to be adapted in management concepts, systems and mechanisms, so as to effectively improve the quality of risk management of commercial banks.

Method of measuring default probability

In recent years, western commercial banks, especially those advanced banks, have made full use of the latest research results of modern mathematical statistics, explored many methods to measure the probability of customer default, and made great achievements. Looking at the practical development of default probability measurement, it shows the following characteristics and trends: from ordinal default probability to cardinal default probability, the measurement of default probability is more and more specific; From the measurement of default probability of a single loan to the joint default probability of a combined loan; From only considering the borrower's own microeconomic characteristics to considering the influence of macroeconomic factors; From static measurement based on historical data to dynamic measurement based on prediction; From single technology to multi-technology, the measurement technology of default probability is more modern, reflecting interdisciplinary, and the measurement is more scientific and accurate.

The measurement methods of default probability of western commercial banks can be summarized into four categories:

1. Measurement method based on historical data of internal credit rating, that is, commercial banks and rating companies take the average value of historical default probability as the corresponding default probability of enterprises under different credit ratings according to historical credit rating data accumulated for a long time;

2. The measurement method based on option pricing theory is a credit monitoring model established by KMV company in the United States by using option pricing theory, also known as KMV model. It is a forward-looking dynamic model, which is mainly suitable for measuring the default probability of publicly listed companies;

3. The measurement method based on actuarial science is to estimate the expected default probability in recent years with the tool of insurance thought;

4. Measurement method based on risk-neutral market principle. The so-called risk-neutral market means that in the market where assets are traded, all investors are willing to get the same expected return from any risk-free assets, and all asset prices can be calculated by discounting the expected future cash flow of assets at the risk-free interest rate. Compared with the historical transfer probability, the risk neutral model gives a forward-looking default prediction.

Limitations of international representative credit risk assessment model in China

Since China's entry into WTO, the operation mode of China's market economy has been accelerated in line with international standards, and how China's credit rating industry can be in line with international standards has also been challenged. It is imperative to explore and choose a foreign evaluation model suitable for the China market, and some domestic scholars have also made beneficial research on it. Here, after applying some representative foreign evaluation models to the China market for empirical research, we collected some problems and defects found by the academic circles, so as to facilitate the follow-up research work.

1, Z-Score credit risk assessment model

Z model is a method to predict the possibility of company default or bankruptcy by selecting five key financial ratios and giving them certain parameters (weights).

These include:

X 1= working capital/total assets

X2= (undistributed profit+capital reserve)/total assets

X3= pre-tax profit and interest/total assets

X4= market value of equity/book value of debt.

X5= turnover/total assets

Take z value as the critical value, if it is less than the critical value, debt default will occur.

Empirical research shows that the Z model has the following three defects: First, the model is accurate for a few industries in listed companies, and the parameters of many industries need to be adjusted. Second, we need to use some accounting information or other indicators to replace the data that non-listed companies and small companies can't obtain the equity value, and finally get the expected default probability through comparative analysis. This may affect the accuracy of calculation to some extent. Third, it needs to be adjusted according to the situation of domestic financial market on the basis of Z value, which ordinary decision makers can't do.

2.KMV credit risk assessment model

KMV model is based on the option pricing theory, and its starting point is based on the assumption that any information of the company can be reflected in the stock price and its fluctuation. When the expected value of the company's stock falls below a certain level (default point value) due to fluctuations, the company will default on its debts. In this model, the creditor's rights held are regarded as risk-free creditor's rights minus a put option. On this basis, the default distance is calculated, and the empirical default probability is estimated by combining the data of listed companies. Although KMV model is more sensitive than the traditional default probability estimation system based on accounting data analysis, its adaptation conditions are stricter. From the results, it is more suitable for listed companies in mature capital markets. Obviously, at present, China does not have the conditions to promote KMV mode.

3.CreditMetrics credit risk assessment model

The model is based on the assumption that the distribution of debt portfolio value in a certain period (usually one year) has nothing to do with the change of debtor's future credit rating, and the probability of credit rating transfer follows a stable Markov process, that is, the current grade transfer of loans or bonds has nothing to do with its past transfer probability. Although this model has been proved to be an effective credit risk model at present, there are still some problems to be solved. First, this model assumes that the current level migration of loans or bonds has nothing to do with its past migration probability. However, the actual historical data shows that if a debt has defaulted in the past, the probability of its current grade decline is higher than that of the same grade without default; Second, when calculating the VaR value of debt, it is assumed that the probability matrix of grade transfer is stable, that is, the probability of grade transfer between different borrowers and different maturities is constant. In fact, industry, country, business cycle and other factors will have an important impact on the probability matrix of grade transfer. Thirdly, the default model of CreditMetrics model and the measurement of correlation coefficient are based on option pricing theory, which requires high maturity conditions of stock market and authenticity of data.

4. Neural network model

Neural network model is also widely used in the west to estimate the default probability. It relies on the collected data and analyzes a large amount of financial and related information by means of mathematical statistics, thus establishing a default estimation model. This model still has limitations in empirical research. First, with the innovation of technology and financial tools, it is increasingly difficult for the limited data in financial statements to truly reflect the financial situation and operating results of enterprises, especially for high-tech enterprises, non-financial factors occupy more and more weight; Secondly, because the distortion of accounting information in domestic enterprises is still serious, the use of distorted data input model will inevitably lead to the deviation of calculation results.

From the empirical research results of several foreign credit risk assessment models in China, we can see that China's securities market is immature (the company's value cannot be reflected through the market), the disclosure of market information is very limited, the authenticity of financial data is not high, and there are no objective conditions such as a large-capacity credit information database that rating agencies can use, so it cannot be used. However, as the achievement of modern econometrics, the extensive application of credit risk assessment model in developed market economy countries proves its objectivity and scientificity. The development of market economy in China is still in the primary stage, and there is still a big gap in market maturity compared with developed market economy countries. The above-mentioned evaluation model still lacks the basic conditions for application in China.

Research and Development of Default Probability in China

For China's banking industry, internal rating is still in the primary stage, which is short and irregular. The infrastructure construction of default database and transfer matrix is almost blank. The credit rating of loan enterprises is more used for customer selection and risk early warning, and has not yet developed in the direction of deeper risk quantitative management. Therefore, China's commercial banks and rating companies should actively create conditions to strengthen the measurement of customer default probability, so as to effectively improve the level of credit risk management.

First of all, with reference to the definition of the new Basel Capital Accord, scientifically define the concept of enterprise default. At present, there is no consistent and clear standard of company default in China. In order to be in line with the international practice, it is suggested that the China banking industry define the concept of enterprise default as: within a certain period of time (usually one year), as long as any secondary, suspicious or loan loss occurs in the loan business of an enterprise, it is regarded as a defaulting enterprise.

Second, accelerate the establishment of default probability measurement model infrastructure-default database. China's banking industry can establish a qualified default database by establishing a financial data filter for enterprises, checking the authenticity of financial statements submitted by enterprises, and laying a solid foundation for measuring the default probability. The bank credit registration consultation system established by the People's Bank of China provides a massive loan database information platform for the banking industry in China. On this basis, domestic banks can give full play to the advantages of system data resources, constantly improve system information, and then establish their own default database.

Third, strengthen the research, development and application of default probability measurement model. Based on the particularity of China's banking environment and historical practice, the default probability model that can be applied by western commercial banks may not be suitable for China commercial banks. However, we can learn from the measurement ideas, methods and processes of these default probability models, and combine data accumulation to realize the transition from simple models to complex models. For example, we can use the credit measurement model to measure the transfer probability and default probability of each credit rating in the current year according to the accumulation of rating result data in the current year, and then form the measurement of the internal credit rating transfer matrix, and then adjust it continuously with the increase of annual data. In this way, after a period of accumulation, we can establish our own internal transfer matrix model.

In addition, considering the actual credit situation of China's loan enterprises, the measurement of default probability of each credit grade in the transfer matrix model should not only consider the influence of industry and economic periodicity, but also consider the influence of region, scale and the nature of enterprise ownership.