CN110110981B - Credit rating default probability measure and risk early warning method - Google Patents

Credit rating default probability measure and risk early warning method Download PDF

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CN110110981B
CN110110981B CN201910344162.XA CN201910344162A CN110110981B CN 110110981 B CN110110981 B CN 110110981B CN 201910344162 A CN201910344162 A CN 201910344162A CN 110110981 B CN110110981 B CN 110110981B
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邹杨
韦鹏程
蔡银英
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Abstract

The invention belongs to the technical field of financial information data management, and discloses a credit rating default probability measurement and risk early warning method; the method comprises the following steps: mining effective data, and measuring and calculating default probability; constructing a default loss rate prediction model, and checking the consistency of rating results; and constructing a binary response risk early warning model, and realizing an early warning strategy by means of a data mining technology. Through research and application of a credit rating mathematical model, a credit rating system with strong feasibility capable of using data demonstration is finally formed by utilizing a data mining technology, and effective practical experience is obtained. Meanwhile, research results can be cooperated with financial industry and credit enterprises to provide credit products and technical services for the credit enterprises and provide data reference for trading decisions of market bodies, thereby contributing to credit demands and development of credit industry.

Description

Credit rating default probability measure and risk early warning method
Technical Field
The invention belongs to the technical field of financial information data management, and particularly relates to a credit rating default probability measurement and risk early warning method.
Background
Currently, the closest prior art:
the core problem of credit rating is the study of default probability, which is divided into two aspects, namely the measure of default probability and the evaluation of default probability. The former is to solve the problem of how to measure and calculate the default probability; the latter study is aimed at analyzing the relevant factors and their importance in determining, influencing and probability of breach.
The study of the measure of the probability of breach can be classified into the following categories: a credit rating default probability based on credit rating history, a "cardinality" default rate based on option pricing theory, a measure of an insurance actuarial default probability, and a measure of a default rate based on Risk Neutral (RN) market. Representative studies include: a Creditmetrics model for expressing the default probability in the form of a transfer matrix; a Creditportfoliio View model for calculating the condition default probability by incorporating the macroscopic economic factors; a default monitor model (KMV) which is a default prediction model using option pricing theory; a mortality model based on the life insurance idea and a Creditisk + model developed based on an actuarial framework. The default probability assessment research mainly comprises the following analysis methods: univariate analysis, multivariate analysis, modern evaluation methods. Representative studies include: evaluation of univariate analysis of default probability typically represented by the "forecast of operational failure in financial ratio" study; a ZETA scoring model is established according to a multivariate discriminant analysis thought; a model for credit assessment of consumer loan applicants is applied using cluster analysis. Currently, a lot of proofs research uses a Logit regression model and a neural network model which assume that default events are generated and obey Logistic distribution. The default probability model taking the neural network technology as the core does not require the assumption of probability distribution, and can deeply mine the hidden correlation among the predictive variables, so that the problem of non-normal and non-linear credit risk analysis can be effectively solved. However, the neural network model faces the difficulties that the network structure is difficult to determine and overfit, and the prediction capability and the model application of the neural network model to the default of a new sample are greatly influenced.
With the increasing demand of the economic market for credit systems and the continuous and deep segmentation of credit rating research, the need for effective data collection and efficient data processing is more urgent. With the recent progress of data mining technology, the ability to mine and analyze data is becoming more and more important in credit rating research. Data mining refers to the process of extracting information and knowledge of potential application value from a large amount of random actual data. The goal is to discover from the large amount of data the rules or relationships between data that are hidden behind it, thereby serving the decision. The data mining technology converges different disciplines and cross fields of database, artificial intelligence, statistics, visualization, parallel computation and the like. Its classical process is divided into: definition of questions, data collection and preprocessing, execution of data mining algorithms, and interpretation and evaluation of results. Data mining has the advantages of no need of depending on assumed conditions, capability of processing large-scale data and the like, and is widely applied to financial analysis and risk prediction, and particularly, the data mining is concentrated in the fields of credit card auditing, stock market analysis, investment decision and the like. Because the financial data is mostly large-sample and high-dimensional data, the data mining is good at processing multivariable large data, the method for depicting the financial market risk by using the data mining algorithm is scientific and reasonable, and the data mining technology provides a plurality of feasible technical means for a risk early warning system. Therefore, the credit rating theory is checked by means of a data mining technology, a risk management system is perfected, a risk early warning strategy is realized, theoretical research and scientific technology are fused and promoted, and the development trend of credit rating research is realized.
The financial industry plays a significant role in national economy, and the perfection and development degree of a financial system are directly related to whether the national economy can be continuously and healthily developed. The risk is an inherent feature of the financial industry, and is more and more interesting along with the deepening development of the finance. The objective existence of financial risk has spawned a need for financial risk management due to the random volatility of the financial market. Credit rating serves as an important participant in financial risk management, and plays a role in specialized risk disclosure. The credit rating is an assessment of the ability and trustworthiness of the debt subject to pay for the debt in due, for example, order, is an assessment of the risk of debt repayment, and is primarily intended to reveal the credit risk of the debt issuer, reducing the transaction cost and investment risk.
The credit rating industry of China is built along with the market economic system and gradually developed from the end of the 80 s of the 20 th century. Through the development of the recent 30 years, although the credit rating industry of China makes great progress, the credit rating industry is still in a starting stage compared with international industry, and due to the reasons that a rating model is not mature enough, a rating technology is relatively lagged behind and the like, the credit rating development process faces the following three problems:
1. the fit between the historical default rate and the contemporaneous default probability is not ideal, because the reform of financing system in China and the development of bond market, the credit activities of economic main bodies become frequent day by day, huge database scale is generated, and the difficulty in mining effective data to count the historical default rate is increased. And because the rating system, method or actual operation of the rating mechanism is not stable enough, and the influence of factors such as macroscopic economic environment is added, the acquired data has strong randomness, which provides a new challenge for calculating default probability. The fact shows that the default rate counted according to the historical credit data is different from the real default probability in the same period, and the real data is not ideal to fit with the original default probability measurement model. And the default probability is the core problem of measuring and calculating the credit risk. The rating authority defines corresponding credit rating levels for liability entities of different attributes, which are based on the probability of default. The default probability value enables the credit rating result to have more intuitive explanatory power, provides more accurate measurement about the risk level, provides a foundation for risk monitoring and management, and a large number of credit risk models are based on calculating the default probability. Therefore, the breach probability measure is the problem of the first study, and it is necessary to improve the original measure model and reduce the difference between the historical breach rate and the contemporaneous breach probability.
2. The lack of consistency check of rating results is from 1841 that the first commercial credit rating institution Louis Tappan in the world is established in New York to the present, graders, statisticians, mathematicians and software programmers create countless credit rating models, develop a great amount of rapid rating software, and China's rating institutions also introduce a lot of advanced rating software, but in the actual credit rating work, people pay more attention to rating results, but lack of consistency check and correction of rating results. The reason for this is that the macroscopic economy and the financial environment change rapidly, and the deviation between the rating result and the actual situation is inevitable, and the deviation is objective. The difficulty of the consistency check of the rating results is the consistency check between the credit quality of the bond and the credit rating thereof. The key index of credit quality of bonds is the expected loss rate of bonds (the expected loss rate is default probability x default loss rate), wherein the factors influencing the default loss rate are complex, and the factors have correlation, so that the expected loss rate can be accurately obtained only by scientifically screening out the main factors influencing the default loss rate by using a correlation mathematical analysis method and establishing a prediction model. The consistency check between the credit quality and the credit grade is achieved, the modification of the rating result and the rating model is perfected, and scientific and correct credit rating judgment is made, so that the method is an essential link of a credit rating system.
3. The tracking rating work is difficult, the risk early warning is delayed, the tracking rating means that a credit rating organization still closely pays attention to related change information of a rated person after the rating work is finished, and the purpose is to ensure that the credit risk of the rated person can be continuously tracked and revealed in the project duration, so that the failure of the rating result is avoided. However, in China, the application range of the credit rating result is narrow, the evaluated body does not pay attention to the change of the credit condition after obtaining the rating result, the credit data collected by a credit rating mechanism is only limited to the number of indexes before rating, and the data loss in the later period is serious, so that the tracking and rating work is difficult, the timeliness of the rating information is low, and the risk early warning is delayed. The construction and implementation of a risk early warning system need the participation of a plurality of discipline theories and technologies. Financial engineering, mathematical models, financial management, computers, information technology and the like are all important subject fields supporting the operation and development of a risk early warning system. With the improvement of the financial investment market on the risk early warning requirement, the credit risk early warning index system is perfected, and the realization of an early warning strategy by means of a corresponding data mining technology is an urgent need in the big data era.
The participation of the data mining technology provides a more diversified data processing technical means and concept for credit rating research, and a rating system tends to develop towards a multi-angle and multi-level direction. The trend of mutual fusion and mutual promotion between the credit rating and the data mining technology is further strengthened, and the seamless connection of the credit rating and the data mining technology is the real objective requirement and is the inevitable process of converting scientific theories into practical operations.
In summary, the existing credit rating techniques are:
(1) the enterprise independent development credit rating system calculates default probability of data by using the existing mathematical model;
(2) the credit rating factor system mainly takes quantitative data and uses a mathematical model for quantitative analysis;
(3) most credit rating systems adopt a principal component analysis method to perform data dimension reduction processing on multiple factors of credit rating, and then factor analysis is used for ranking credit levels;
(4) and the enterprise makes judgment according to the credit level result.
In summary, the problems of the prior art are as follows:
(1) the neural network model network structure is difficult to determine and overfit, and the prediction capability and the model application of the neural network model network structure to new sample default are greatly influenced.
(2) The default rate counted according to the historical credit data is different from the real default probability in the same period, and the real data is not fit with the original default probability measurement model ideally.
(3) In the actual credit rating work, people pay more attention to the rating result, but the consistency check and correction of the rating result are lacked.
(4) And the data loss at the later stage is serious, so that the tracking and rating work is difficult, the timeliness of rating information is low, and the risk early warning is delayed.
(5) The randomness of variables in financial markets is rarely considered by the original mathematical model, and a rating system, a rating method or actual operation of a rating mechanism is not stable enough;
(6) part of the actual credit rating work is qualitative index factors, and if influence of the qualitative factors on the rating is ignored, the accuracy of default probability measure is reduced;
(7) the principal component analysis algorithm loses information of a part of original data in the process of dimension reduction, and through data processing of the principal component analysis algorithm, if the contribution rate is more than 85%, the system considers that the subsequent data result has statistical value, but the accuracy and the reliability of rating are directly influenced by the lost data information;
the difficulty of solving the technical problems is as follows:
(1) a method of investigating a breach probability p measured by a breach rate;
(2) determining major factors affecting the loss rate of default;
(3) and (3) realizing a data mining technology of an early warning strategy.
The significance of solving the technical problems is as follows:
(1) adding a parameter lambda on the basis of the original Mudy model, and considering the influence of random fluctuation of non-credit factors on default probability in the model;
(2) adding qualitative index factors, setting a feasible region of the qualitative index, and establishing a default loss comprehensive index system;
(3) a credit rating mathematical model is improved, and the accuracy and reliability of default probability measure are improved;
(4) the consistency check of the evaluation result is perfected, and the model establishment, the model application and the model correction are closed by a rating result correction model algorithm;
(5) a rating early warning system is established by utilizing a classification idea of supervised learning in machine learning, and an early warning strategy is realized by using a data mining technology.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a credit rating default probability measurement and risk early warning method.
The invention is realized in such a way, and provides a credit rating default probability measurement and risk early warning method.
The credit rating system is composed of a default probability measure calculation module, a credit rating index system module, a supervised learning mathematical model visualization module and a data query and rating report generation module.
The default probability measure calculation module can realize data acquisition and default probability measure calculation through a data mining technology, and the data acquisition and default probability measure calculation comprises data loading, parameter setting and default probability measure calculation.
The credit rating index system module can realize the storage of qualitative index quantitative index source data, the collinear analysis of data columns, the pretreatment of original data, including data cleaning, data integration, data transformation, data specification and the consistency check of credit quality and credit grade.
The supervised learning mathematical model visualization module can realize the prediction of a credit rating result, including the comparison of data results of logistic regression, a support vector machine and a neural network model, the comparison of an optimal rating result and default probability measure, and the further revision of a Mudy model.
The data query and rating report generation module can realize the functions of data backup, data query and print preview and the function of early warning of later default.
The data query and rating report generation module further comprises:
step 1: screening out three factors (m (R), n (R), l (R)) influencing the default rate by utilizing a data mining technology, and setting parameters lambda, lambda belongs to [0, 1 ∈ [)]Calculating out the default rate p (R) by using the modified Mudy model and the chi of the distribution family2Fitting a test method, testing the probability distribution condition of p (R), measuring default probability by digital characteristics, and dividing credit grades according to the default probability value, wherein the grades are divided into M types, and M is an integer from 1 to 5. M-1 denotes a credit level AAA, M-2 denotes a credit level AA, M-3 denotes a credit level a, M-4 denotes a credit level BBB, and M-5 denotes a credit level BB. The larger the default probability value is, the larger the M value is, and the larger the default risk is.
Step 2: extracting qualitative index data and quantitative index data of a sample by using a data mining technology, storing source data, calculating Pearson correlation coefficient analysis colinearity of a data column, setting a correlation coefficient r, wherein r belongs to (0,1), and if the obtained Pearson correlation coefficient is greater than r, performing variable transformation xij=xi/xjAnd eliminating collinearity, and then carrying out data preprocessing such as data cleaning, data integration, data transformation, data reduction and the like.
And step 3: firstly, setting a credit level based on an default probability value as a contemporaneous credit level, then carrying out consistency check on the credit level and a historical credit level, if the consistency check is not passed, returning to the step 1 for revising the parameter lambda, if the consistency check is passed, taking a factor influencing LGD in a credit evaluation index system as an explanatory variable, taking the contemporaneous credit level based on the default probability value as an explained variable, respectively testing samples by using a logistic regression, a Support Vector Machine (SVM) and a neural network model, comparing the accuracy and the recall rate, visualizing an ROC curve and an AUC value, and selecting an optimal model as a later credit rating early warning model by the system.
And 4, step 4: and setting the credit grade M to be 2, assigning 0 to the class A as a risk-free credit grade, assigning 1 to the class B as a risk credit grade, constructing a binary response risk early warning model, and realizing an early warning strategy by means of a data mining technology. And backing up data, generating a credit rating visual report, storing the credit rating visual report as a WORD or PDF document, and printing a credit evaluation result.
The credit rating default probability measurement and risk early warning method comprises the following steps:
step one, mining effective data, and measuring and calculating default probability;
step two, constructing a default loss rate prediction model, and checking the consistency of rating results;
and step three, constructing a binary response risk early warning model, and realizing an early warning strategy by means of a data mining technology.
Further, the first step is to mine effective data, and the method for measuring and calculating the default probability comprises the following steps: the probability of breach p is measured by the rate of breach. Since it is difficult to accurately calculate the default probability corresponding to the credit rating in advance, the default probability is estimated using the default rate. The default rate refers to the actual historical frequency with which the debtor fails to fulfill his financial obligations, i.e., the occurrence of a default, as defined by the contract. And the default probability refers to the possibility of default of the debtor in a given period in the future. And obtaining the default rate through tracking and analyzing the credit rating historical data of the rating institution, and estimating the default probability from the default rate probability distribution condition.
Further, the method for calculating the default probability specifically comprises the following steps:
the first step, screening three factors (m (R), n (R) and l (R)) influencing the default rate by utilizing data mining, and calculating the default rate p (R);
second, using chi of the distribution group2And fitting a test method, testing the p (R) probability distribution condition, and measuring the default probability by using the digital characteristics.
Further, the first step of calculating the default probability is specifically:
and improving the Mudy model dynamic group to obtain the annual default rate p (R) of the distributors with the grade R as follows:
Figure BDA0002041740150000081
wherein m (R): the number of violations occurring in an issuer with a rank R; n (R): the original number of publishers with a rank R; l (R): the number of issuers with a rank of R who are revoked due to non-credit related reasons; λ: and determining a feasible interval of the proportionality coefficient lambda.
1) If the default probability does not change along with the time, the default rate p (R) of the large sample in t yearstThe default rate p (R) of the weighted average of T years approximately follows a normal distribution, having
Figure BDA0002041740150000082
Wherein p: a probability of breach; m ist: number of publishers in t years; m: the number of the distributors is counted in T years,
Figure BDA0002041740150000083
2) if the default probability fluctuates with time but the annual fluctuations are independent of each other, then
Figure BDA0002041740150000084
Wherein σ: wave factor
3) If the default probability fluctuates with time and there is continuity in the fluctuation, the average default rate DR over the entire lifetime is approximately in accordance with the following normal distribution:
Figure BDA0002041740150000085
wherein the content of the first and second substances,
Figure BDA0002041740150000086
θ: different degrees of continuity.
Further, the second step of calculating the default probability specifically includes:
and (3) testing the probability distribution condition of p (R) by using a Chi 2 fitting test method of the distribution family, and measuring the default probability by using the numerical characteristics. If it is
Figure BDA0002041740150000091
The probability of breach p is the mathematical expectation, and p is estimated by maximum likelihood estimation.
The specific process is as follows:
first, hypothesis H is examined0:p(R)tThe possible probability density function is
Figure BDA0002041740150000092
Then, the estimated values of mu, sigma are obtained by the maximum likelihood estimation method
Figure BDA0002041740150000093
Then divide omega to get event A1,A2,…,AkFrequency of calculation fiAnd
Figure BDA0002041740150000094
thereby calculating out
Figure BDA0002041740150000095
Taking the significance level a if
Figure BDA0002041740150000096
Then refuse H0. If H is accepted0Then probability of breach
Figure BDA0002041740150000097
Further, the second step of constructing a default loss rate prediction model, and checking consistency of the rating results specifically includes:
the consistency check of the credit rating result means that the principal default probability of the bond issuer has consistency with the credit rating thereof, and the credit quality of the bond has consistency with the credit rating thereof. For the bond issuer, the consistency between the default probability and the credit level of the main body does not relate to specific default loss, so the default rate is estimated mainly by using the historical data of the default of the main body, and consistency check is carried out. Collecting, sorting and screening subject default historical data, and establishing a database is the premise of checking default probability and credit level consistency. In the quality and level consistency check link, because the credit quality of the bond contains more factors and the inherent relationship is complex, and the simple examination of the default probability of the bond is not enough to describe the actual credit performance, the consistency check of the bond should take the expected loss rate (i.e. the default probability x the default loss rate) as the main examination factor. The size of the loss rate of default LGD is measured and calculated, and is not only influenced by factors of a debt subject, but also closely related to the specific design of a debt project, and the factors influencing the LGD comprise project factors (such as settlement priority, collateral products and the like), company factors (such as total assets, total liabilities and the like), industry factors (such as recovery rate and the like) and macroscopic economic cycle factors (such as economic indexes and the like). The key point of checking the consistency of the rating results is to research and determine default loss rate influence factors, establish a default loss rate prediction model and check the consistency of quality and grade from the perspective of bond credit quality. For the establishment of the default loss rate prediction model, the factor analysis method can be utilized to determine main factors influencing the default loss rate LGD, and the multivariate regression is used to fit the quantitative relation between the factors and the default loss rate, so that the default loss rate is predicted, the expected loss rate is predicted, and the consistency of the rating results is checked.
Further, there are two aspects to checking the consistency of the rating results: the first is the violation probability and credit level consistency, and the second is the credit quality and credit level consistency. The difficulty is the consistency check between the credit quality of the bond and the credit grade of the bond, because the credit quality contains many factors such as default probability, loss severity and grade transfer risk, and the internal relationship is complex. Therefore, the expected loss rate (the expected loss rate is the default probability × the default loss rate) is used as a factor mainly for examining the bond consistency check, and the research and determination of the factor affecting the default loss rate LGD become a key problem of the research.
Further, the third step of constructing a binary response risk early warning model, and implementing an early warning strategy by means of a data mining technology specifically comprises:
the purpose of tracking the subject being evaluated is to ensure that the credit risk of the subject is continuously revealed for the life of the project. If a subject is tracked and recorded for a period of time, and the main economic activity data in the period of time is collected, and the duration is t, the probability that the subject will violate before 1+ t is high, which is a problem that the risk probability is frequently answered. Such a problem is also understood to mean that the risk probability of duration t is the risk of a breach between t and 1+ t. Survival analysis reveals when the subject under evaluation may violate the contract. The risk and survival curves provide a snapshot of the life cycle (i.e., the performance of the joint session) of the subject being assessed for the liability. And establishing an early risk early warning model in a later period of the publication of the rating result, and detecting a default warning signal.
Aiming at the construction and realization of a binary response early warning model, a special form of a linear regression model, namely a logistic regression analysis method aiming at qualitative variables, is adopted. However, the linear regression problem is converted into logistic regression, and the probability can be estimated by multiplying a string of likelihoods by using the thought similar to a naive Bayes model, and then the probability is converted into the probability. The key point of constructing the binary response early warning model is to estimate the default probability according to the duration of the subject to be evaluated. Since the probability ranges from 0 to 1 and the probability ranges from 0 to + ∞, the method is utilized
Figure BDA0002041740150000111
The probability is converted to a probability. Then taking the logarithm of probability to generate a function from negative infinity to positive infinity, and establishing a regression equation with the logarithm of probability as a target variable:
Figure BDA0002041740150000112
the obtained logistic function is used for calculating default probability of duration, and subsequent economic activity data of the debt subject can be fitted and predicted by a logistic regression analysis model.
In summary, the advantages and positive effects of the invention are:
the measurement of default probability is the most core problem in a credit rating system, is a necessary input variable for quantifying credit risk, and has very important significance for the management of the credit risk. Digging effective data related to the default rate under the background of big data, and calculating the historical default rate; improving a dynamic group of the Mudy model, researching the relation between the default rate and the default probability, checking the rationality of the default rate and the default probability by using actual data, and simultaneously determining a feasible interval of a proportionality coefficient; the method for measuring the default probability is researched by utilizing the probability distribution condition of the default rate, the probability of default of the evaluated subject is estimated according to the default probability, and the credit risk exposed to default is reduced.
The binary response risk early warning model is constructed, a credit evaluation system can be used for carrying out credit risk pre-control, when measures are still taken to reduce exposure risk, a warning signal of default is detected, and a warning is sent out, so that the occurrence of involuntary default of a debt subject is effectively solved, and the loss caused by credit risk is reduced to the minimum degree. The method comprises the steps of constructing a binary response risk early warning model, detecting whether the subject to be evaluated violates at t time after the snapshot date in a snapshot set of all subjects to be evaluated at a given time point, selecting an early warning strategy for the subject to be evaluated close to a contract period or a subject to be evaluated low by using a data mining technology, and reminding the subject to be evaluated of the debt of the contract to fulfill the contract, so that the risk of involuntary violation is reduced.
Through research and application of a credit rating mathematical model, a credit rating system with strong feasibility capable of using data demonstration is finally formed by utilizing a data mining technology, and effective practical experience is obtained. Meanwhile, research results can be cooperated with financial industry and credit enterprises to provide credit products and technical services for the credit enterprises and provide data reference for trading decisions of market bodies, thereby contributing to credit demands and development of credit industry.
The innovation point of the invention is that an effective way for the probability of default measure is created by the probability distribution of the default rate, and an algorithm is realized by using a data mining technology. The data mining technology is closely combined with the credit rating theory, so that the practical technology and the scientific theory form a development situation of mutual fusion and mutual promotion. Penetration of data mining technology makes application and demonstration of credit rating models possible, and feasibility of model inspection is enhanced. On the basis of the existing credit rating algorithm, research and development and test work of a credit risk early warning model and a related matched model are improved and innovated, so that the credit quality corresponding to the credit rating can be more scientifically and accurately quantified.
(1) Because the Mudy model is added with the parameter lambda, the influence of the randomness of non-credit factors on the default probability measure is considered, so that the model is more widely applied;
(2) the qualitative index and the quantitative index are combined, a credit evaluation factor index system is established, and factors considered by credit evaluation are more comprehensive;
(3) data are collected by using a data mining technology, and a credit evaluation result is more real and reliable under a big data background;
(4) by using a supervised learning algorithm in machine learning, the predicted rating accuracy is higher, and the credit rating early warning strategy is more accurate.
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FIG. 1 is a block diagram of a credit rating system according to an embodiment of the present invention.
In the figure: 1. a breach probability measure calculation module; 2. a credit rating index system module; 3. a supervised learning mathematical model visualization module; 4. and a data query and rating report generation module.
Fig. 2 is a flowchart of a method for measuring a probability of breach of credit rating and warning risk according to an embodiment of the present invention.
Fig. 3 is a flowchart of a method for calculating a default probability according to an embodiment of the present invention.
FIG. 4 is a diagram of the training set results of the SVM confusion matrix according to the embodiment of the present invention.
FIG. 5 is a diagram illustrating the result of the SVM confusion matrix test set provided by the embodiment of the present invention.
Fig. 6 is a diagram of a training set result of a neural network confusion matrix according to an embodiment of the present invention.
FIG. 7 is a diagram illustrating the results of a confusion matrix testing set of neural networks according to an embodiment of the present invention.
FIG. 8 is a diagram illustrating the results of the test set of the logistic regression confusion matrix provided by the embodiment of the present invention.
Fig. 9 is a graph showing the result set from the training of the confusion matrix of the neural network according to the embodiment of the present invention.
FIG. 10 is a schematic diagram of an embodiment of the present invention
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The following detailed description of the principles of the invention is provided in connection with the accompanying drawings.
As shown in fig. 1, the credit rating system provided in the embodiment of the present invention is composed of a default probability measure calculation module 1, a credit rating index system module 2, a supervised learning mathematical model visualization module 3, and a data query and rating report generation module 4.
The default probability measure calculation module 1 can realize data acquisition and default probability measure calculation through a data mining technology, and the data acquisition and default probability measure calculation comprises data loading, parameter setting and default probability measure calculation.
The credit rating index system module 2 can realize the storage of qualitative index quantitative index source data, the collinear analysis of data columns, the pretreatment of original data, including data cleaning, data integration, data transformation, data specification, and the consistency check of credit quality and credit grade.
The supervised learning mathematical model visualization module 3 can predict the credit rating result, including comparison of data results of logistic regression, support vector machine and neural network model, comparison of the optimal rating result and default probability measure, and further revision of the mucdi model.
The data query and rating report generation module 4 can realize the functions of data backup, data query, print preview and early warning of later default.
The data query and rating report generation module 4 further comprises:
step 1: screening out three factors (m (R), n (R), l (R)) influencing the default rate by utilizing a data mining technology, and setting parameters lambda, lambda belongs to [0, 1 ∈ [)]Calculating out the default rate p (R) by using the modified Mudy model and the chi of the distribution family2Fitting a test method, testing the probability distribution condition of p (R), measuring default probability by digital characteristics, and dividing credit grades according to the default probability value, wherein the grades are divided into M types, and M is an integer from 1 to 5. M-1 denotes a credit level AAA, M-2 denotes a credit level AA, M-3 denotes a credit level a, M-4 denotes a credit level BBB, and M-5 denotes a credit level BB. The larger the default probability value is, the larger the M value is, and the larger the default risk is.
Step 2: extracting qualitative index data and quantitative index data of a sample by using a data mining technology, storing source data, calculating Pearson correlation coefficient analysis colinearity of a data column, setting a correlation coefficient r, wherein r belongs to (0,1), and if the obtained Pearson correlation coefficient is greater than r, performing variable transformation xij=xi/xjAnd eliminating collinearity, and then carrying out data preprocessing such as data cleaning, data integration, data transformation, data reduction and the like.
And step 3: firstly, setting a credit level based on an default probability value as a contemporaneous credit level, then carrying out consistency check on the credit level and a historical credit level, if the consistency check is not passed, returning to the step 1 for revising the parameter lambda, if the consistency check is passed, taking a factor influencing LGD in a credit evaluation index system as an explanatory variable, taking the contemporaneous credit level based on the default probability value as an explained variable, respectively testing samples by using a logistic regression, a Support Vector Machine (SVM) and a neural network model, comparing the accuracy and the recall rate, visualizing an ROC curve and an AUC value, and selecting an optimal model as a later credit rating early warning model by the system.
And 4, step 4: and setting the credit grade M to be 2, assigning 0 to the class A as a risk-free credit grade, assigning 1 to the class B as a risk credit grade, constructing a binary response risk early warning model, and realizing an early warning strategy by means of a data mining technology. And backing up data, generating a credit rating visual report, storing the credit rating visual report as a WORD or PDF document, and printing a credit evaluation result.
As shown in fig. 2-3, the method for measuring the probability of breach of credit rating and warning risk provided by the embodiment of the present invention includes:
s101: mining effective data, and measuring and calculating default probability;
s102: constructing a default loss rate prediction model, and checking the consistency of rating results;
s103: and constructing a binary response risk early warning model, and realizing an early warning strategy by means of a data mining technology.
Further, the first step is to mine effective data, and the method for measuring and calculating the default probability comprises the following steps: the probability of breach p is measured by the rate of breach. Since it is difficult to accurately calculate the default probability corresponding to the credit rating in advance, the default probability is estimated using the default rate. The default rate refers to the actual historical frequency with which the debtor fails to fulfill his financial obligations, i.e., the occurrence of a default, as defined by the contract. And the default probability refers to the possibility of default of the debtor in a given period in the future. And obtaining the default rate through tracking and analyzing the credit rating historical data of the rating institution, and estimating the default probability from the default rate probability distribution condition.
Further, the method for calculating the default probability specifically comprises the following steps:
s201: screening three factors (m (R), n (R) and l (R)) influencing the default rate by utilizing the data mining data, and calculating the default rate p (R);
s202: using χ of distribution group2And fitting a test method, testing the p (R) probability distribution condition, and measuring the default probability by using the digital characteristics.
Further, the first step of calculating the default probability is specifically:
and improving the Mudy model dynamic group to obtain the annual default rate p (R) of the distributors with the grade R as follows:
Figure BDA0002041740150000151
wherein m (R): the number of violations occurring in an issuer with a rank R; n (R): the original number of publishers with a rank R; l (R): the number of issuers with a rank of R who are revoked due to non-credit related reasons; λ: a proportionality coefficient, determining a feasible range of lambda;
1) if the default probability does not change along with the time, the default rate p (R) of the large sample in t yearstThe default rate p (R) of the weighted average of T years approximately follows a normal distribution, having
Figure BDA0002041740150000152
Wherein p: a probability of breach; m ist: number of publishers in t years; m: the number of the distributors is counted in T years,
Figure BDA0002041740150000153
2) if the default probability fluctuates with time but the annual fluctuations are independent of each other, then
Figure BDA0002041740150000154
Wherein σ: wave factor
3) If the default probability fluctuates with time and there is continuity in the fluctuation, the average default rate DR over the entire lifetime is approximately in accordance with the following normal distribution:
Figure BDA0002041740150000161
wherein the content of the first and second substances,
Figure BDA0002041740150000162
θ: different degrees of continuity.
Further, the second step of calculating the default probability specifically includes:
using χ of distribution group2And fitting a test method, testing the p (R) probability distribution condition, and measuring the default probability by using the digital characteristics. If it is
Figure BDA0002041740150000163
The probability of breach p is its mathematical expectation and p can be estimated using maximum likelihood estimation.
The specific process is as follows:
first, hypothesis H is examined0:p(R)tThe possible probability density function is
Figure BDA0002041740150000164
Then obtaining the estimated value of mu, sigma by maximum likelihood estimation method
Figure BDA0002041740150000165
Then divide omega to get event A1,A2,…,AkFrequency of calculation fiAnd
Figure BDA0002041740150000166
thereby calculating out
Figure BDA0002041740150000167
Taking the significance level a if
Figure BDA0002041740150000168
Then refuse H0. If H is accepted0Then probability of breach
Figure BDA0002041740150000169
Further, the second step of constructing a default loss rate prediction model, and checking consistency of the rating results specifically includes:
the consistency check of the credit rating result means that the principal default probability of the bond issuer has consistency with the credit rating thereof, and the credit quality of the bond has consistency with the credit rating thereof. For the bond issuer, the consistency between the default probability and the credit level of the main body does not relate to specific default loss, so the default rate is estimated mainly by using the historical data of the default of the main body, and consistency check is carried out. Collecting, sorting and screening subject default historical data, and establishing a database is the premise of checking default probability and credit level consistency. In the quality and level consistency check link, because the credit quality of the bond contains more factors and the inherent relationship is complex, and the simple examination of the default probability of the bond is not enough to describe the actual credit performance, the consistency check of the bond should take the expected loss rate (i.e. the default probability x the default loss rate) as the main examination factor. The size of the loss rate of default LGD is measured and calculated, and is not only influenced by factors of a debt subject, but also closely related to the specific design of a debt project, and the factors influencing the LGD comprise project factors (such as settlement priority, collateral products and the like), company factors (such as total assets, total liabilities and the like), industry factors (such as recovery rate and the like) and macroscopic economic cycle factors (such as economic indexes and the like). The key point of checking the consistency of the rating results is to research and determine default loss rate influence factors, establish a default loss rate prediction model and check the consistency of quality and grade from the perspective of bond credit quality. For the establishment of the default loss rate prediction model, the factor analysis method can be utilized to determine main factors influencing the default loss rate LGD, and the multivariate regression is used to fit the quantitative relation between the factors and the default loss rate, so that the default loss rate is predicted, the expected loss rate is predicted, and the consistency of the rating results is checked.
Further, there are two aspects to checking the consistency of the rating results: the first is the violation probability and credit level consistency, and the second is the credit quality and credit level consistency. The difficulty is the consistency check between the credit quality of the bond and the credit grade of the bond, because the credit quality contains many factors such as default probability, loss severity and grade transfer risk, and the internal relationship is complex. Therefore, the expected loss rate (the expected loss rate is the default probability × the default loss rate) is used as a factor mainly for examining the bond consistency check, and the research and determination of the factor affecting the default loss rate LGD become a key problem of the research.
Further, the third step of constructing a binary response risk early warning model, and implementing an early warning strategy by means of a data mining technology specifically comprises:
the purpose of tracking the subject being evaluated is to ensure that the credit risk of the subject is continuously revealed for the life of the project. If a subject is tracked and recorded for a period of time, and the main economic activity data in the period of time is collected, and the duration is t, the probability that the subject will violate before 1+ t is high, which is a problem that the risk probability is frequently answered. Such a problem is also understood to mean that the risk probability of duration t is the risk of a breach between t and 1+ t. Survival analysis reveals when the subject under evaluation may violate the contract. The risk and survival curves provide a snapshot of the life cycle (i.e., the performance of the joint session) of the subject being assessed for the liability. And establishing an early risk early warning model in a later period of the publication of the rating result, and detecting a default warning signal.
Aiming at the construction and realization of a binary response early warning model, a special form of a linear regression model, namely a logistic regression analysis method aiming at qualitative variables, is adopted. However, the linear regression problem is converted into logistic regression, and the probability can be estimated by multiplying a string of likelihoods by using the thought similar to a naive Bayes model, and then the probability is converted into the probability. The key point of constructing the binary response early warning model is to estimate the default probability according to the duration of the subject to be evaluated. Since the probability ranges from 0 to 1 and the probability ranges from 0 to + ∞, the method is utilized
Figure BDA0002041740150000181
The probability is converted to a probability. Then taking the logarithm of probability to generate a function from negative infinity to positive infinity, and establishing a regression equation with the logarithm of probability as a target variable:
Figure BDA0002041740150000182
the obtained logistic function is used for calculating default probability of duration, and subsequent economic activity data of the debt subject can be fitted and predicted by a logistic regression analysis model.
In summary, the principle of the credit rating default probability measure and risk early warning method is as follows: firstly, collecting, sorting and storing original data of economic activities of debt subjects by utilizing R language, and establishing a database. Secondly, calculating Z statistic and a corresponding accompanying probability P value by using single sample S-K test, judging the overall distribution condition of the data according to a P-value law principle, correspondingly obtaining an estimated value of a parameter mu according to the digital characteristics of random variable default rate and a maximum likelihood estimation method, and obtaining the default probability P. Thirdly, the software implementation of the default loss rate prediction model follows the factor analysis principle and thought to obtain the molecular score coefficient, and the regression model is set and checked in the EViews statistical software to predict the default loss rate. The software implementation of the binary response risk early warning model can firstly reassign 0 and 1 to qualitative variables, set condition early warning names, detect a database default warning signal and automatically prompt an evaluated subject or a low-evaluation subject reaching a contract fulfillment critical point.
The main contents of the invention are linked, the rules are clear, and the scheme is reasonable. The research content has a certain depth and breadth, and the demonstration of the research scheme can meet the requirement of the actual work of the current credit rating so as to meet the international convention. The data mining technology can meet the requirements of research, development and test work of matched models through hardware and software. The statistical software related to the project can directly import data in an Excel format, so that the data collection and the database establishment are facilitated, and the R language provides a plurality of high-level management functions and can process a large amount of data. The flexibility, security and ease of use of the present invention provide good conditions for rating model programming.
The invention makes a reasonable project implementation progress plan, selects a research team with rich scientific research and teaching experience, establishes a good cooperative relationship and ensures the smooth execution of the project. The team members of the project teach three by pairs, teach two instructors and help to teach one, and a reasonable research echelon is formed. Six members are statistical training guide teachers of academies, are engaged in theoretical research and practical training work of random processes and application statistics for many years, and have very strong data processing capacity and software editing capacity.
The library of the second college of Chongqing has ordered digital resources such as databases of Chinese and foreign periodicals, which is beneficial for project group members to look up some related documents and provides a complete new-looking-up condition for the implementation of the project. A statistical laboratory is established in the mathematics and information engineering system of the Chongqing second academy of academic and vocational study, statistical series software is equipped, and the statistical laboratory cooperates with the soft and cool company to develop financial mathematics experimental training projects, so that a higher platform is provided for cross and innovation research of computers, mathematics and financial multidisciplines. This provides good software and hardware support for the implementation of the project. The research result can further cooperate with credit rating institutions and financial industries to provide credit products and services and provide data reference and suggestion for trading decisions of market subjects.
The invention is further described with reference to specific examples.
Example (b):
data mining 1020 effective sample data, selecting partial data of an index system, setting M to be 2, performing binary classification prediction test, and testing the samples by using a Support Vector Machine (SVM), a neural network and a logistic regression model respectively to obtain the following results:
Figure BDA0002041740150000191
(1) the SVM operation result analysis is shown in fig. 4 and fig. 5, and table one and table two.
TABLE 1 SVM test set evaluation criteria indexes
Figure BDA0002041740150000192
Figure BDA0002041740150000201
TABLE 2 various evaluation standard indexes of SVM training set
Figure BDA0002041740150000202
(2) The operation results of the neural network are analyzed as shown in fig. 6 and 7, and tables three and four.
TABLE 3 evaluation criteria indexes of neural network test set
Figure BDA0002041740150000203
TABLE 4 evaluation criteria indexes of neural network training set
Figure BDA0002041740150000204
(3) The results of the logistic regression runs were analyzed as shown in fig. 8 and 9, and in table five and table six.
TABLE 5 various evaluation criteria indexes of logistic regression test set
Figure BDA0002041740150000211
TABLE 6 various evaluation criteria indexes of logistic regression training set
Figure BDA0002041740150000212
As can be known from SVM model, neural network model and logistic regression model algorithm, in the three algorithms, the result of data shows that the algorithm for establishing the logistic regression model has better fitting and statistical significance.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (4)

1. A credit rating breach probability measurement and risk early warning method is characterized by comprising the following steps:
step one, mining effective data, and measuring and calculating default probability;
step two, constructing a default loss rate prediction model, and checking the consistency of rating results;
constructing a binary response risk early warning model, and realizing an early warning strategy by means of a data mining technology;
the first step is to mine effective data, and the method for measuring and calculating default probability comprises the following steps: the default probability p is measured by the default rate; the default rate refers to the actual historical frequency of debtors failing to fulfill their financial obligations, i.e., the occurrence of a default, as defined by the contract; the default probability refers to the possibility of default of the debtor in a given period in the future; obtaining default rate through tracking and analyzing the credit rating historical data of the rating organization, and estimating default probability from the probability distribution condition of the default rate;
the method for calculating the default probability specifically comprises the following steps:
the first step, screening three factors m (R), n (R) and l (R) which influence the default rate by utilizing data mining, and calculating the default rate p (R);
secondly, testing the probability distribution situation of p (R) by using a Chi 2 fitting test method of a distribution family, and measuring the default probability by using digital characteristics;
constructing a default loss rate prediction model, and checking the consistency of the rating results specifically comprises the following steps:
the consistency check of the credit rating result means that the principal default probability of the bond issuer is consistent with the credit rating of the bond issuer, and the credit quality of the bond is consistent with the credit rating of the bond issuer; for bond issuers, the agreement between the subject's default probability and the credit rating does not relate to a specific loss of default; collecting, sorting and screening subject default historical data, and establishing a database is the premise of checking default probability and credit level consistency; in the quality and grade consistency inspection link, the expected loss rate is taken as a main investigation factor in the consistency inspection of the bonds; the size of the LGD for calculating the default loss rate is not only influenced by factors of a debt subject, but also closely related to the specific design of a debt project, and the factors influencing the LGD comprise project factors, company factors, industry factors and macroscopic economic cycle factors;
the consistency of the rating results is checked, the key is to research and determine default loss rate influence factors, establish a default loss rate prediction model and check the consistency of quality and grade from the perspective of credit quality of bonds; aiming at the establishment of a default loss rate prediction model, determining main factors influencing default loss rate LGD by using a factor analysis method, predicting default loss rate by using a quantitative relation between multiple regression fitting factors and default loss rate, predicting expected loss rate according to the default loss rate, and checking the consistency of a rating result;
constructing a binary response risk early warning model, and realizing an early warning strategy by means of a data mining technology specifically comprises the following steps: estimating the probability of default according to the duration of the subject; because the probability has a value range of 0-1 and a probability range of 0- + ∞, the probability is utilized
Figure FDA0003096251890000021
Converting the probability into probability; then taking the logarithm of probability to generate a function from negative infinity to positive infinity, and establishing a regression equation with the logarithm of probability as a target variable:
Figure FDA0003096251890000022
the obtained logistic function is used for calculating default probability of duration, and subsequent economic activity data of the debt subject can be fitted and predicted by a logistic regression analysis model.
2. The method for measuring the probability of breach and early warning of risk in a credit rating as claimed in claim 1, wherein the first step of calculating the probability of breach is specifically: and improving the Mudy model dynamic group to obtain the annual default rate p (R) of the distributors with the grade R as follows:
Figure FDA0003096251890000023
wherein m (R): the number of violations occurring in an issuer with a rank R; n (R): the original number of publishers with a rank R; l (R): the number of issuers with a rank of R who are revoked due to non-credit related reasons; λ: a proportionality coefficient, determining a feasible interval of the proportionality coefficient lambda;
1) if the default probability does not change along with the time, the default rate p (R) of the large sample in t yearstAnd the default rate p (r) of the T-year weighted average follows approximately a normal distribution, as follows:
Figure FDA0003096251890000024
wherein p: a probability of breach; m ist: number of publishers in t years; m: the number of the distributors is counted in T years,
Figure FDA0003096251890000031
2) if the default probability fluctuates with time but the fluctuation of each year is independent, then:
Figure FDA0003096251890000032
wherein σ: a fluctuation factor;
3) if the default probability fluctuates with time and there is continuity in the fluctuation, the average default rate DR over the entire lifetime is approximately in accordance with the following normal distribution:
Figure FDA0003096251890000033
wherein:
Figure FDA0003096251890000034
θ: different degrees of continuity.
3. The method for measuring the probability of breach and early warning of risk in a credit rating as claimed in claim 1, wherein the second step of calculating the probability of breach specifically comprises:
testing the probability distribution of p (R) by using X2 fitting test method of distribution family, and measuring default probability by using digital characteristics
Figure FDA0003096251890000035
The default probability p is the mathematical expectation, and p is estimated by a maximum likelihood estimation method;
the specific process is as follows:
first, hypothesis H is examined0:p(R)tThe possible probability density functions are:
Figure FDA0003096251890000036
then, the estimated values of mu, sigma are obtained by the maximum likelihood estimation method
Figure FDA0003096251890000037
Then divide omega to get event A1,A2,…,AkFrequency of calculation fiAnd
Figure FDA0003096251890000038
thereby calculating out
Figure FDA0003096251890000039
Taking the significance level a if
Figure FDA0003096251890000041
Then refuse H0(ii) a If H is accepted0Then probability of breach
Figure FDA0003096251890000042
4. The method for credit rating breach probability measure and risk pre-warning of claim 1, wherein the consistency of the verification rating result is two-fold: the first is the violation probability and credit level consistency, and the second is the credit quality and credit level consistency.
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