基于极小极大算法的信用评级模型

doi:10.16381/j.cnki.issn1003-207x.2024.1777

摘要/Abstract

摘要：

信用评级旨在区分不同风险水平的贷款人，为银行信贷投资提供依据。目前，一些高信用等级的企业频频出现违约，表明信用等级和信用风险之间存在不匹配现象。为缓解这种不匹配，现有研究多以穷举所有等级方式划分客户信用等级，其计算复杂度过高，划分结果具有一定随机性。本文使用违约损失率来表征信用风险，并引入三个准则进行信用等级划分，这些准则旨在要求贷款客户的信用等级应与其违约损失率相匹配；进而，从理论上提出一种极小极大信用等级划分算法解决信用等级错配问题。本文首先讨论了该算法解的存在性并证明了解的唯一性，其次证明了所提算法的计算复杂度为 $O (n 2)$ ，最后严格证明了该算法可以使信用等级与信用风险严格匹配。利用2017笔中小企业和2044笔农户真实信贷数据，实证结果表明：本文提出的极小极大信用等级划分算法可以将信用等级与违约风险严格匹配，并降低高信用等级的违约损失。该算法可为研究人员和金融机构在信用风险评估方面提供新的思路和参考。

关键词: 信用评级, 信用等级划分, 违约损失率, 极小极大算法

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

中图分类号:

F830.56

陆阳, 石宝峰. 基于极小极大算法的信用评级模型[J]. 中国管理科学, 2025, 33(2): 28-37.

Yang Lu, Baofeng Shi. Min-max Algorithm for Matching Credit Ratings with Loss Given Default[J]. Chinese Journal of Management Science, 2025, 33(2): 28-37.

图/表 9

表1

表2

表3

2157笔小企业信贷信用评级结果"

1	2	极小极大算法		Shi 等(2020)		Chai 等 (2019)
1	2	3	4	5	6	7	8
等级	等级	样本量	LGD_k	样本量	LGD_k	样本量	LGD_k
1	AAA	11	0.00%	127	0.07%	102	0.09%
2	AA	67	0.02%	518	0.60%	478	0.65%
3	A	1	0.04%	756	0.63%	493	0.88%
4	BBB	48	0.17%	312	0.77%	283	0.08%
5	BB	523	0.59%	256	1.03%	298	0.80%
6	B	751	0.63%	81	1.52%	227	1.10%
7	CCC	312	0.77%	56	2.36%	174	1.50%
8	CC	256	1.03%	22	5.58%	73	1.75%
9	C	188	3.32%	29	8.92%	29	8.92%
计算复杂度		$O (n 2)$		$O (n 8)$		$O (n * 迭代次数)$

表3

图1

图2

表4

图3

图4

表5

2044笔农户信贷数据信用等级划分结果"

1	2	极小极大算法		Shi 等(2020)		Chai 等 (2019)
1	2	3	4	5	6	7	8
等级	等级	样本量	LGD_k	样本量	LGD_k	样本量	LGD_k
1	AAA	30	0.00%	81	0.01%	340	0.37%
2	AA	141	0.01%	310	0.42%	460	0.63%
3	A	371	0.40%	190	0.63%	333	0.78%
4	BBB	675	0.80%	130	0.67%	338	0.99%
5	BB	557	1.04%	310	0.72%	281	0.84%
6	B	88	1.28%	130	0.93%	157	2.54%
7	CCC	90	3.55%	160	1.27%	87	3.68%
8	CC	29	4.07%	190	1.66%	42	4.45%
9	C	63	9.29%	543	2.05%	6	30.35%
计算复杂度		$O (n 2)$		$O (n 8)$		$O (n * 迭代次数)$

表5

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贷款人编号	应收本息和R_i	应收未收本息L_i	银行A的排名	银行B的排名
Loan 1	1	0	1	10
Loan 2	1	0.1	2	9
Loan 3	1	0.2	3	8
Loan 4	1	0.3	4	7
Loan 5	1	0.4	5	6
Loan 6	1	0.5	6	5
Loan 7	1	0.6	7	4
Loan 8	1	0.7	8	3
Loan 9	1	0.8	9	2
Loan 10	1	0.9	10	1

借款人编号	应收本息和（元）	应收未收本息和（元）	信用得分
Loan 1	103910	0	99.99
Loan 2	103915	0	99.97
…	…	…	…
Loan 1226	104263	316.5536	89.17
Loan 1227	103871.5	0	89.17
…	…	…	…
Loan 2156	103995	132.4311	46.61
Loan 2157	10387.15	0	44.53

借款人编号	应收本息和（元）	应收未收本息和（元）	信用得分
Loan 1	52613.75	0	96.54
Loan 2	84294.4	0	96.32
…	…	…	…
Loan 1218	54620	52894.48	88.69
Loan 1219	31557.6	0	88.69
…	…	…	…
Loan 2043	16345.125	6943.66	60.57
Loan 2044	55505	55330.36	59.90

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