《保险研究》20230701-《“偿二代”下非寿险最低资本相关矩阵情景分析——基于最接近相关矩阵的正交试验》（张连增、庄源）

［摘   要］“偿二代”下非寿险风险采用相关系数矩阵进行聚合，出于审慎监管和资本管理的目的需要对该相关系数矩阵假设进行情景测试。受限于相关系数矩阵的半正定性要求，以往研究的情景测试仅对风险完全相关、完全不相关情形得到最低资本估计，得出的结论与实际情况存在差异。针对上述问题，本文使用2022年第2季度中国保险市场58家财险公司的最低资本披露数据，在最接近相关矩阵修正下开展正交试验，生成多个压力情景下各家财险公司的最低资本并进行极差分析与异质性分析。本文结果表明：第一，使用完全相关和完全不相关情形进行情景分析可能过分夸大了最低资本的敏感性；第二，在监管部门系统性调高相关系数矩阵元素时，主营业务为特定业务线(车险、财产险、船货特险、责任险和短期意外险)且相对分散的财险公司资本压力较大；第三，财险公司业务结构极大影响最低资本对单一相关系数的敏感性；第四，与传统的矩阵分解法相比，最接近相关矩阵不涉及对矩阵特征值的讨论，能给出更合理的敏感性结果；第五，在进行相关矩阵情景分析时，正交试验法相对于随机模拟方法的时间成本更小，两种方法下的经验分布尾部特征存在一定差异。本文的研究结论展示解释了相关矩阵假设变动时财险公司最低资本敏感度的异质性，为“偿二代”的假设变动测试提供了进一步的参考。

［关键词］情景分析；偿二代；保险风险最低资本要求；最接近相关矩阵；正交试验

［基金项目］本文得到教育部人文社会科学研究基金(编号：22YJC790034)、天津市研究生科研创新项目(编号：2022SKY038)和南开大学研究生院《定量风险管理》课程建设基金的资助。

［作者简介］张连增，南开大学金融学院精算学系教授，博士生导师；庄源，南开大学金融学院精算学系硕士研究生。

A Scenario Analysis of Correlation Matrix for Minimum Capital Requirement of Non-Life Insurance Risk under C-ROSS—Orthogonal Experiment with Nearest Correlation Matrix Theory

ZHANG Lian-zeng,ZHUANG Yuan

Abstract：Non-life risks under C-ROSS are aggregated using correlation matrix,and scenario testing of correlation assumptions is required for prudential supervision and capital management purposes.Due to the nature of the correlation matrix,the scenario testing on previous studies only provides minimum capital estimates under perfectly correlated and perfectly uncorrelated scenarios,which generates very different results from actual situations.To address these issues,this paper uses the minimum capital disclosure data of 58 Chinese P&C insurance companies in 2022Q2 to conduct an orthogonal experiment with the modified nearest correlation matrix to generate the minimum capital requirement of each P&C insurance company under multiple scenarios,and executes range analysis and heterogeneity analysis.The results of this paper show that:(1) The sensitivity of minimum capital may be overstated by using perfectly correlated and perfectly uncorrelated scenarios;(2) When the regulatory authorities systematically lift the elements of correlation matrix,the capital pressure is higher for P&C insurers whose main businesses include automobile insurance,property insurance,marine and cargo insurance,liability insurance and short-term accident insurance,and whose main businesses are relatively dispersed;(3) The business structure of P&C insurers significantly affects the sensitivity of minimum capital to a single correlation coefficient;(4) The nearest correlation matrix method does not involve discussions on eigenvalues and gives more reasonable sensitivity results than the traditional spectral decomposition method;(5) When performing the correlation matrix scenario analysis,the orthogonal experiment method is less time costly compared to the stochastic simulation method and there are some differences in the tail characteristics of the empirical distribution generated by these two methods.The findings of this paper explain the heterogeneity of the minimum capital sensitivity of P&C insurers when relevant matrix assumptions change,and provide further reference for the testing of C-ROSS.

Key words：scenario analysis;C-ROSS;minimum capital requirement;nearest correlation matrix;orthogonal experiment