Pricing Longevity Bonds Based On Stochastic Mortality Model

In recent years, with the development of social economy and the improvement of living standard, the mortality rates of our population showed a declining trend, resulting in serious population aging and the population average life expectancy. The growth of life expectancy significantly extend the payment period of the pension, annuity and other products, which results in a substantial increase in costs and longevity risk. Longevity risk increases pension liabilities, leading to a huge funding gap which not only bringing the crisis to the government and life insurance companies, but also threatening to social development.Therefore, using various channels to control and hedge longevity risk becomes an urgent problem.It is a trend of financial innovation to using the capital markets for securitization of longevity risk. Through the issuance of longevity bonds, whose yields relate to the mortality rates, we can transfer the longevity risk from the life insurance companies to capital market. As a new kind of financial derivatives, the accurate pricing of longevity bonds can improve the ability to resist risks. Thus, it becomes the focus of the study to accurately price longevity bonds in recent years. Since the coupon payments of longevity bonds related to the survival index of the underlying population, while the survival index usually obtained through the mortality model, it becomes a key step to establish a mortality model to forecast the mortality rates in the pricing process. In addition, because of longevity bonds transacted in the context of incomplete market, the traditional discussion of the complete market pricing will inevitably biased. In view of these problems, this paper studies the following aspects and obtains conclusions:(1) Considering the uncertainty caused by changes in time, we use the dynamic stochastic model established by Babel, Bomsdorf and Schmidt to forecast future mortality rates of our population, and then compare with the commonly used model--Lee-Carter model. The results shows that Babel, Bomsdorf and Schmidt model fits the data of our population and the prediction is better.(2)Using Wang Transform, the distortion of the probability distribution of the pricing method is applied to bond pricing. With this method, the theoretical price is closer to the market price, achieving the pricing of the incomplete market. Wang conversion equation has simple expressions, and thus has an advantage in practical applications.(3) We design a longevity bond by using the data forecasted by the stochastic model of mortality.Using Wang Transform, we calculate the price of longevity bond. The analysis of parameter sensitivity further illustrates the mortality model plays an important role on the accuracy of the pricing of longevity bonds.In summary, by using stochastic mortality model and Wang Transform method, we improve the accuracy of the pricing of longevity bonds and enhance the effectiveness of mortality prediction models. The research aims to help enhancing the longevity risk management and the good development of financial and insurance industries.