Scenario Analysis of Correlation Matrix for Minimum Capital Requirement of Non-Life Insurance Risk under C-ROSS (in Chinese)
Abstract
Non-life risks under C-ROSS are aggregated using correlation matrix, and scenario testing of correlation assumption is required for prudential supervision and capital management purposes. Due to the nature of the correlation matrix, the scenario testing in previous studies only provides minimum capital estimates under independence correlation matrix, comonotonicity correlation matrix and the correlation matrix respectively proposed by regulators, which generates very different results from actual situations. To address these issues, this paper uses the solvency disclosure data of 58 Chinese P&C insurance companies in 2022Q2 to conduct an orthogonal experiment with the modified nearest correlation matrix, generating the minimum capital requirement of each P&C insurance company under multiple scenarios and give 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 increase the elements of correlation matrix, 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 not overly concentrated; (3) The business structure of P&C insurers significantly affects the sensitivity of minimum capital to some single correlation coefficient.; (4) The nearest correlation matrix method does not involve discussion of eigenvalues and gives more reasonable sensitivity results than the traditional spectral decomposition method and (5) When performing the scenario analysis of correlation matrix, 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, and provide further reference for the testing of C-ROSS.
