Abstract:

Credit rating aims to distinguish lenders with different risk levels and provide a basis for bank loans. Nowadays， credit ratings are prone to problems such as ratings overrated and lacking differences. The fact that some high-credit-level enterprises default indicates a mismatch between credit ratings and credit risk. To solve this mismatch， loss given default （LGD） is used to measure credit risk and establish three criteria： 1.The credit ratings should match their average loss given default. 2. Minimize the loss given default for high-credit-level ratings. 3. Without increasing the loss given default， the ratings should contain as many loan customers as possible. Next， it is demonstrated that credit scores are closely related to credit ratings. Therefore， the research hypothesis is that the credit score used in credit rating is positively correlated to the borrower’s credit level. With the constraints of these three criteria， a novel min-max algorithm is developed to solve the mismatch problem. The uniqueness of the solution of the proposed algorithm is further proved. The computational complexity of the min-max algorithm as O（n²）is then derived. By mathematics induction， it is proved that criterion 2 and criterion 3 imply criterion 1， so this algorithm can theoretically make credit ratings consistent with credit risk. To test the proposed algorithm， it is compared with the other two credit rating methods using 2，017 small and medium enterprises （SMEs） loans and 2，044 farmer loans. The results indicate the proposed algorithm can match the credit ratings with loss given defaultwelland lower high credit levels’ loss given default. The proposed min-max algorithm may bring new ideas and perspectives for researchers and financial institutions on credit risk evaluation.

Key words: credit rating, credit risk, loss given default, min-max algorithm