Copula models of economic capital for life insurance companies

Abstract

The objective of the paper is to introduce a copula methodology of economic capital modeling, which is practically applicable for life insurance companies. Copula methods make it possible to address multiple dependent risk factors including both investment and underwriting risks in the framework of a portfolio approach. We identify a relevant set of asset and liability variables, and suggest a copula model for the joint distribution of these variables. Estimates of economic capital are constructed via VaR and TVaR calculations based on the tails of this joint distribution. This approach requires ARIMA and copula model selection followed by Monte Carlo simulation of the time series of the joint asset/liability portfolio. Models are implemented in open source software (R and MS Excel) and tested using historical and simulated asset/liability data. The results are applied to the construction of a software tool which can be utilized for customization and direct user application. The novelty of the approach consists in estimating interdependent underwriting and investment risks in one multivariate model taking into account short-term (daily or monthly) fluctuations of the market. In particular, we address the challenges that life insurance companies face in the low interest environment, using the market data for the 15-year period 2003–2018.