Securitization of Longevity Risk: Pricing under Stochastic Mortality Model with Tranching Design

在這篇研究中，我們利用分券的概念設計長命風險債券。首先，保險公司和特殊目的機構之間簽訂一再保險契約，這個再保險契約與合成型擔保債券憑證中的信用違約交換合約相似。特殊目的機構依照損失率的大小，將長命風險債券切割成四個不同等級的債券並予以發行給投資人。我們利用Feller過程配適美國的生命表資料衡量未來30年的長命風險，及計算在考慮長命風險的市場價格之下，轉換過後的存活機率分配。證券化分券的例子將於文中詳細介紹。We utilize the securitized tranche technique to design a security for transferring longevity risk to the capital market. Our structure follows the concept of synthetic CDO. The reinsurance contract, which is similar to a CDS (Credit Default Swap), is first set between the insurer and the SPV. Then, the longevity bond is constructed and divided into four tranches according to the portfolio loss rate distribution. The longevity risk is modeling under a non mean-reverting Feller process introduced in Luciano and Vigna (2005). We value the longevity risk and calculate the transformed distribution under Wang’s method to consider the market price of longevity risk. A securitization tranching example is illustrated and the mortality information is based on the US mortality data observed in Human mortality data base.I. Introduction 6 A. Longevity Risk 6 B. Advantages of Securitization 6 C. Mortality Linked Securities in The Market 7 D. Other Survivor Derivatives 8 E. Mortality Model 10 F. Agenda 11 II. The Stochastic Mortality Model 12 A. Survivor Probability 12 B. Calibration to the US Mortality Table 14 III. Securitization of Longevity Risk 17 A. Valuation of Longevity Risk 17 B. Wang Transform 19 C. Design of Longevity Bond 21 IV. Conclusion and Discussions 26 References 2