基于双指数跳跃扩散模型的长寿债券定价研究

Pricing Longevity Bonds based on Double Exponential Jump Diffusion Model

伴随着人均寿命的延长,人口老龄化带来的长寿风险问题成为世界各国必须面对的重要课题。长寿风险对各国的社保部门、寿险公司和政府造成了严重影响,如何有效地管理长寿风险成为学术界研究的焦点。鉴于已有长寿债券研究模型在考虑人口死亡率正负向不对称跳跃方面的不足,本文在Lee-Carter模型的基础上,采用双指数跳跃扩散模型对死亡率的正负向不对称跳跃进行刻画,并运用经典的CIR利率模型对长寿债券进行贴现,然后通过引入风险中性定价法给出不完全市场中的债券定价,使得定价更贴近真实市场。对人口死亡数据进行实证分析的结果表明,本文模型度量长寿风险的能力要明显优于已有模型。因此,应用本文模型进行债券定价,不仅可以提供更合理的定价,还可以提高寿险公司应对长寿风险的能力,从而促进寿险业在我国的进一步发展。

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.