Abstract: With the extension of life expectancy, the countries in the whole world must face the fact that aging population brings longevity risk. Longevity risk has put severe impacts on security departments, insurance companies and the governments in the world. Therefore how to manage it effectively has become the focus of study by the academic society. In view of the fact that the research model of longevity bonds has not considered the positive and negative asymmetry jump of population mortality, and in order to hedge the risk of longevity, based on Lee-Carter framework, a double exponential jump diffusion model is introduced to measure the positive and negative asymmetry jump of mortality rates, the interest rate is described with CIR. And in order to make the pricing of bonds closer to the real market, the risk neutral pricing is used to price the bond in the incomplete market. Empirical analysis with the population death data shows that the ability of this model is significantly better than the existing model when measuring longevity risk. Therefore, the use of this model for bond pricing, not only can provide a more reasonable pricing, but also can improve the life insurance companies to deal with the risk of longevity, then can promote the further development of life insurance industry in China.

Key words: longevity bonds, CIR model, double exponential jump diffusion model, neutral risk