A Research On The Application Of Copula Function In Valuation Of Insurance Companies

The insurance investment is an important source of the profits for insurance companies. With the recovery of insurance industry in China, it has experienced a rapid growth. Many companies have set up their branch companies in China, so the competition is more and more intense. In addition to provide customers with high quality insurance products and an enhanced level of customer services, lower price is the key for insurance companies to improve their competitiveness. With a lenient regulation on insurance product rates, many companies offer many products with lower price, this means less.profit, so the company has to resort to dependent on investment for more profit.There are two ways to increase investment income. On the one hand, it is very important to improve the efficiency of investment of insurance companies as much as possible to find investment opportunities with a higher rate of return on investment. With insurance regulatory commission widening the investment channels of insurance funds, it will provide more choice of investment products, but also increased the risk of investment. In order to ensure the safety of the insurance funds and the principle of liquidity, various insurance companies invest in almost similar channels, so their investment rates are almost the same. The net investment rate of return of China Ping An Life Insurance Company in2011is only4.5%, this is equivalent to two years of the bank deposit interest rates, so it is difficult to gain an advantage on the efficiency of investment. In addition, we can also raise the company’s revenue by expanding the scale of investment. Insurance companies get income before the payment which is quite different from other industries. For the life insurance companies, this gap between income and payment even lasts for several decades, this part can be used for produce more income through investment. CIRC supervises the reserve very strictly, because reserve acts s a pivotal position in the insurance company, it is withholding part of obligations in the future, if there is not adequate reserve, that will poses a great threat to the company’s solvency. The interests of the policyholders will not be guaranteed, so we must ensure the investments safety and liquidity, and only a portion of the reserve can be invested to generate higher investment income.Actually, as will be discussed in our paper, most insurance companies have much more reserve funds than needed. It is because that various types of products of a company are not entirely correlated. For example, if one product has suffered more serious losses, this may not happen to other types of insurance, therefore the reserve for these types of insurance becomes part of "overlapping". Our paper will show that for the life insurance companies, this part of the overlap is up to16.21%. And for the Non-life companies, this part of the overlap will reached up to10.95%. If we put this part of the "extra" fund into the higher-return yield, this will undoubtedly inject great vitality to insurance companies and greatly enhance the rate of return on investment.In order to calculate the overestimated reserve ratio of the insurance company, we need a new tool to overthrow the various insurance related assumptions, and calculate the specific relevance of the various types of insurance. Insurance data is often asymmetric, skewed to the right and thick tailed, so the traditional correlation measure is difficult to be applied in insurance industry, especially the intricate relationship of the various types of insurance, which will inevitably lead to measurement errors, or even the opposite conclusion. Fortunately, the Copula function can effectively measure the correlation between the different types of insurance. It not only can calculate the joint distribution of the different types of insurance, but also can 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 different types of insurance has been estimated, we can roughly estimate the number of reserve, so we pay much attention to the marginal distribution estimating and the selection of the Copula function.