Measuring Economic Capital For Property Insurance Companies: VaR, CVaR And Copula Approach

After decades of rapid development, China’s insurance industry has achieved a great growth. Compared with the insurance companies of developed countries, there is still a big gap in terms of profitability, and other aspects of risk management of our insurance companies. With increasingly complex economic environment, insurance companies in Chain need advanced risk management approach. Through almost 20 years, the Economic Capital becomes one of the most popular ERM tools in global insurance industry.Meanwhile, it is only few years since the introduction of Economic Capital in China. There is no consensus in the measure of Economic Capital. So, in this paper, we focus on the way to measure the Economic Capital of property insurance companies.Underwriting risk is the main risk for property insurance companies, we use Copula function to measures dependence structure between the underwriting business lines. Copula function can not only measure the linear relationship but also depicts the nonlinear relationship between them.This paper consists of six chapters. The rest of this paper is organized as following:Chapter 1: introduction.Chapter 2: the theory of Economic Capital.Firstly, we explained the definition of economic capital, and compared several easily confused concepts. Secondly, the reasons for the importance of economic capital are analyzed. Finally, we introduce the economic capital management system.Chapter 3:the theory of Copula function and risk measure. First, we introduce the definition of Copula function and the classification of it.Then the relationship between Copula function and several rank correlation coefficient is followed. Finally, the advantages and disadvantages of the VaR and CVaR are compared.Charper4:The Economic Capital is estimated using Archimedean Copula. Archimedean Copula model has no limit of the marginal distribution and is able to measure the dependency structure between two random variables. It’s easy to calculate the joint distribution function and the relationship between random variable. First, the marginal distribution functions are fitted by the Crystal Ball. Then the joint distribution function of the motor vehicle insurance and other insurance is calculated. We identify the type of copula that best fits the given application data and perform a goodness of fit test to assess the adequacy of the copula model selected. The results suggest that the Gumbel Copula is better than the other two to describe the dependence structure. Finally, the distribution function of the total loss ratio is fitted. And Economic Capital is estimated.Chapter 5:Using the sample of property insurance industry, we examine the impact of different dependence structure between underwriting lines of insurance on the economic capital measured by Value-at-Risk (VaR) and CVaR. Elliptical Copula can be a useful technique to capture dependence structure where extreme events occur simultaneously. We identify the type of copula that best fits the given application data and perform a goodness of fit test to assess the adequacy of the copula model selected. The results suggest that the t copula with v=2 outperforms the other copulas to describe the dependence structure in an insurance setting where underwriting risk factors exists. The result also suggests the incremental diversification benefit in the modeling of underwriting risk, indicating that both risks diversify against one another to some degree.The main features and innovations of this paper include:(1) Copula function can effectively measure the correlation between the different types of insurance. It not only can calculates the joint distribution of the different types of insurance, but also change the Copula function to fit the different performance of correlation between the types of insurance. Measure of correlation between different types of insurance is the focus of this paper. Once the correlation between the types of insurance have been Estimated, we can roughly estimate the reserve number, so we spent a lot of space for the marginal distribution estimating and the selection of the Copula function. (2) The scatter of each of the two business lines by Monte Carlo Simulation method can be directly observed each Copula nature, especially in the tail.