Study On Credit Rating Model Based On Non-linear Interpolation

Small enterprises offer 80% urban employment opportunities, pay 52.2%notational tax revenue and create 58.8% of GDP. Because of the rapid development of Small enterprises, its loan demand is 5.9% and 4.3% higher than large enterprises and medium size enterprises in respectively. The reason of which lies in some particular features of small enterprises, such as not enough disclosure of financial information, not sophisticated corporate governance regulations, that it is not easy for banks to master the realistic performance and position, and afraid of provide funds to small enterprises. But, one of the key reasons for that is there has not a reliable loan decision system particularly suitable to small enterprises. Establish of a small enterprise rating system as the key part in small enterprise loan decision, is a urgent problem that should be solved.The nature of credit rating is to find the relationship between customer information and default risk, in order to determine the loan price of a obligor and estimate the repayment likelihood and the Loss Given Default (LGD).The default discriminatory power of credit rating model is related to the financial market stability. After the subprime mortgage crisis in 2008 which is due to the error in rating, the credit rating blackbox of Moody's is highly controversial. So the default discriminatory power should be the basic requirement during the indicator reducing, indicator weighting, rating which are the key of credit rating. The key of credit rating is to identifying default risk, otherwise no matter how popular, the authority of the credit rating system is unreasonable. Therefore, building a credit rating system with strong default discriminatory power is essential.Non-linear interpolation based small enterprises credit rating consist by three parts: establishment of small enterprises credit rating indicators system, establishment of small enterprises credit rating indicators weights, establishment of small enterprises credit rating model. First, study on Small enterprises credit rating indicators system is the establishment of a credit rating indicators system that suitable to the features of Chinese small enterprises and is able to significantly discriminate from default samples to non-default ones. Second, by maximizing the target function of default and non-default dispersion and reverse calculate the optimal credits'weights that could construct the optimal credit evaluation formula, and calculate the credit scores for small enterprises. Third, establish a small enterprise credit rating model by making weight translation to "old small enterprise indicators'data" by non-linear interpolation, establish a credit rating model that have the equilibrium credit rating effects and results with "another credit rating system that combines the old and new small enterprises'data together".There are five chapters in this paper. Chapter one is introduction. Chapter two is establishment of small enterprises credit rating indicators system based on significant discriminate principle. Chapter three is establishment of small enterprises credit scoring model based on default and non-default disperse maximization optimal weighting model. Chapter four is study on non-linear interpolation based credit rating model. Chapter five is conclusion and outlook.The major tasks involved in this study are:(1)The features and contributions in establishment of credit rating indicators system includes:establish a small enterprise credit rating model by making weight translation to "old small enterprise indicators'data" by non-linear interpolation, establish a credit rating model that have the equilibrium credit rating effects and results with "another credit rating system that combines the old and new small enterprises'data together". The credit rating model applies weight translation to old samples data, without repeating the process of index reduced and index weight. It makes the new samples get the rating results in consistence with results of "another credit rating system that combines the old and new small enterprises data together" only by putting the index data of new sample in the model. This contribution solves the problem of frequently change credit indicators system if using existing credit rating models. In fact, the credit rating indicators system in anyone of credit rating agencies will not frequently change credit rating indicators system, but keep it stable in a particular long-term period. As while the contribution solves the problem of decide new samples credit ratings applied the index system which reduced by the old samples, that it is ignoring the change of statistic regularity of credit rating when adding the new samples.(2) The features and contributions in obtaining indicators weights includes:the paper establishes a multi-objective regression based on the target function that enables default and non-default credit scores dispersion maximization, which also means the discrimination ability on the default and non-default status maximize. Since the target function has the functional relationship with credit scoring Sj, and has functional relationship with decision variable w,, thus target function has functional relationship with wi. This means wi can be obtained by calculating the optimal result for the multi-objective target function. This solves the shortage of the exiting study that the process of calculate the optimal weights reliance heavily on subjective judgement and not ensuring the maximum default status discrimination ability.(3) The features and contribution in establishment of credit rating indicators system includes:by establishes logistic regression model of indicators xij and default status yi, and find the each indicator's Ward statistical test value sigjo Compare sigj and predetermined significant level a, if sigj<a, it means the jth indicator effect the small enterprises'default status significantly, should be retained, vice versa. By doing this, the indicators that retained could significantly discriminant small enterprise's default status, which solve the shortage in the existing studies that small enterprise credit rating indicators system is not selected depends indicators'discrimination abilities to default status.