The Application Of Fuzzy Discriminant Analysis In Credit Risk Research

Since the reform and opening up of our country, China has achieved rapid development of economy.However, in recent years, there has been decrease in the stability of the financial system due to the manage releasing and financial liberalization.For this purpose, financial institutions continue to deepen their understanding of financial risk research, to improve to improve the accuracy of risk prediction of financial risk models. The research of prediction of credit risk has great practical significance in China even the world.Fuzzy quantification theory is based on the fuzzy multivariate data of several fuzzy groups to make the linear function and give the best separation of the fuzzy groups on the real space. We can determine which of the fuzzy group a new sample should be in. In this article, we want to find out the structure of the decision-making in fuzzy case, that is to build fuzzy linear function of fuzzy groups. Samples are mapped to real space based on the maximal value of variance ratio by the linear function. We give an example to verify the use of fuzzy quantification theory in credit risk analysis.select the appropriate financial ratios of listed companies, use the theoretical approach to determine the type of the credit risk of listed companies.Firstly, we give the definition of fuzzy variance ratioη2. where we have σB2 is called variation between fuzzy groups,σΓ2 is called total variation.Next, making use of maximum value of fuzzy variance ratioη2 to create a linear dis-criminant function. So we haveRewrite the equations into a matrix and vector form:And then rewrite the equation in the form of characteristic equationIn the last equation,η2 and DA are respectively as eigenvalues and eigenvectors Obtained the discriminant function coefficients:In the analysis of the example, select 25 ST companies appeared in China's Shanghai and Shenzhen A share market as samples of default group, select 35 non-ST listed compa-nies as samples of non-default group. Eventually use 60 listed companies'sample data to create a model; Select financial ratios which reflect the company's liquidity, operational ca-pacity, long-term solvency, Profitability, investment income and cash flows, do averages test and association test. Excluding the variables which the significant level more than 0.01 and the financial ratios which have high degree of correlation. Finally, use X1=current liabili-ties/current assets, X2=working capital/revenue, X3=asset/revenue, X4=store/cost of sales as variables of discriminant analysis.The discriminant function is obtained ultimately by used the sample data: y(x)= 0.26305X1+0.17245X2+0.34935X3+0.21515X4.The accuracy of the model checking as follows:the probability of error typeⅠis 6.3 %, the probability of error typeⅠis 16.7%, the overall accuracy is 88.5%. Compared with other discriminant models in our country, this model has a high discriminant accuracy in predicting the credit risk of listed companies, In addition, the probability of error TypeⅡis higher than the probability of error typeⅠin this model, when banks determine the credit risk of listed companies, commit error TypeⅡwill reduce the bank's earnings, But if we commit error Type I,then banks will have losses, for this respect, the model also has relevance.