The Research On Longevity Bonds Pricing Based On Stochastic Mortality Model And Wang Transform

As we all know, the future cash flow of a life insurance company is affected by many uncertain factors, longevity risk is one of the most important factors. In recent years, with the development of China's economic, improvement of medical conditions, as well as the implementation of one-child policy, etc., China's average life expectancy has been increased, the resulting longevity problems brought unprecedented challenges to the life insurance company's annuity business. The traditional risk management methods are difficult to effectively avoid or transfer the risk of longevity, with the growth of longevity risk, life insurance company's solvency and operating conditions will be seriously threatened. With respect to the life insurance company existing limited solvency, funds in the financial markets have great advantages over quantity, liquidity and geographical distribution, through the issuance of financial securities based on longevity risks, such as longevity bonds, the underwriting risks can be transferred to the capital markets, which will become an effective way to avoid the risk of longevity in life insurance companies. Therefore, this article focuses on longevity risk in life insurance business with the help of risk diversification features of capital market to design a longevity bond with empirical analysis.Since the interest payments of longevity bonds are associated with the survival index of the underlying population, and survival index is generally obtained by mortality model. Therefore, how to predict the future mortality in pricing become very critical. Furthermore, since the longevity bond trading is conducted in incomplete markets, the traditional discussion in the full market pricing will inevitably lead to bias. In view of this, the article will be started from the following aspects:(1) Using the life table of China's insurance industry, we will use the non-mean reverting Ornstein-Uhlenbeck process to construct the survival index.(2) Using Wang Transform, the distortion of the probability distribution of the pricing method, to transform the survival index for longevity bond pricing. With this method, the theoretical price is closer to the market value, thus achieving the risk pricing in the incomplete market. Wang Transform equation has simple expressions, which has an advantage in practical applications.(3) Considering the interest rate term structure, the author uses CIR model to portray the characteristics of interest rate. Combined with the preceding converted survival index, this article gives the price of longevity bonds.In summary, the mortality rate stochastic models, Wang Transform and interest rate term structure method used in this paper, improved pricing mode of longevity bonds, enhanced the effectiveness of mortality prediction and provided new ideas for risk management for life insurance companies. Also this helped solve the lack of solvency of life insurance companies, and improve operating safety of life industry, thus contributing to the long-term healthy development of China's insurance industry.