Risk Dependence, Solvency and Stress Testing for Insurers

Abstract

Identifying the relevant risk factors and their interdependence is central to understanding the risk exposures and vulnerabilities of a financial institution. It is needed for risk management, solvency assessment and stress testing. We assemble a unique dataset of risk factors relevant for insurers which are different than for banks, although they share exposure to financial asset risks such as corporate bonds and equities. We use this dataset to estimate risk factor correlations to better understand their dependence structure. We find that correlation between non-financial risk factors is very low (usually insignificant), between financial risk factors on the order of 30-50%, and a mix between the financial and non-financial risk factors. We fit marginal distributions to each of the risk factors, and using a t-copula we present simple simulation application to analyze the solvency of three types of insurers (pure life, pure property and casualty, mixed). We do so using both the point estimates of the correlations as well as the 95% upper and lower bound estimates to explore the sensitivity of stress impact on insurers’ solvency. Our analysis should help provide an empirical basis to regulators in calibrating solvency regimes and to insurers to understand their risk sensitivities and capital needs.