Pricing Models And Empirical Studies Of Mortality-Linked Bonds

The future cash flow of a life insurance company is subject to the impact of many uncertain factors, and one of the most important factors is mortality risk. In recent years, natural or man-made catastrophic events increase unceasingly, life insurance companis have to consider the corresponding numerous death payments. Meanwhile, following the human life extension, the longevity problem brings an unprecedented challenge for pension business of life insurance companys. Because traditional risk management tools cann't evade or transfer the mortality risk effectively. Continued deterioration of the mortality risk will threaten the state of solvency and business operation of life insurance companies. Being compared with the limited solvency of life insurance, capitals in financial markets have many advantages on quantity, fluidity as well as regional distribution. The method to transfer the mortality risk to capital markets via mortality-linked bonds would become an efficient way to hedge the mortality risk. In our courtry, not only disaster but longevity risk is serious, and the life insurance business developments lag behind that of advanced country. Thus, based on the existing studies, this dissertation designs the pricing models of mortality-linked bonds and conducts the empirical study. The results of the related research are as follows:(1) The research improve the description of the mortality index by a jump-diffusion process and comonotonicity theory, constructs a pricing model of castastrophe mortality bond via one-factor Wang thansforme, and makes the empirical analysis. The mortality index model describes jumps of the mortality and a strong positive correlation between mortalities. The model makes up a shortcoming that the existing mortality index models lacked the description of mortality jumps and the correlation. Furtherly, by means of one-factor Wang thansform, the expressions of the bond price in incomplete market can be obtained. Based on this, the dissertation carries out an empirical analysis on the pricing model, and examin the model serviceability from many aspects, such as, calculation of the bond price in examples, sensitivity analysis of main parameters and discussion applicable scope of the pricing model.(2) The research further improves the description of the mortality index by Copula function, constructs a pricing model of the castastrophe mortality bond through two-factor Wang thansform, and carries out the empirical analysis. Here, Archimedean Copula is used to describe the correlation which is more complicated than comonotonicity. In order to reduce the influence of parameter uncertainty, two-factor Wang thansform is applied to price the bond in an incomplete market. And the price of the bond is calculated by Monte Carlo simulation, when the result is not an explicit solution. Based on theoretical research results, the dissertation shows an example of the bond pricing with mortality data of major quake-hit areas in Wenchuan earthquake, carrys out parameter sensitivity analysis, and comparative analysis between two castastrophe mortality bond pricing models of this dissertation.(3) Based on the Ornstein-Uhlenbeck (OU) process with jumps and Cox-Ingersoll-Ross (CIR) model, the research constructs a pricing model of longevity bond through one-factorWang thansform, and carries out the empirical analysis with the data of China's life table. The model coincides with the population characteristics of China and improve inadequate survival function forecast. The term structure of interest rates is considered when price the longevity bond in an incompelete market. The expression of the price model has a good operational feature in empirical analysis.(4) Based on the Feller process with jumps and positive hyperbolic model, the research constructs a pricing model of longevity bond through two-factor Wang thansform. Empirical analysis is conducted further with the data of China's life table. The advantage of this pricing model improves the description of survival index by the Feller process with jumps. And the positive hyperbolic interest rate model is more suitable to describe the characteristics of Chinese money marketIn summary, by considering the characteristics of stochastic mortality and by means of the advantage of the financial market and financial theories, the dissertation improves the accuracy of mortality-linked bonds through a variety of theories and methods, such as interest rate models, Wang thansform, Copula functions, stochastic percesses with jumps, and so on. The pricing models established in this dissertation have many advantages on forecasting mortality and pricing the bond in incompleted market. The results of this dissertation would provide new ideas to manage mortality risk for the life insurance, and help the life insurance solve the prolem of solvency, capital access and liquidity. Further, the research would enhance the security of the company's operating.