1. Extended Logistic Model for Mortality Forecasting and the Application of Mortality-Linked Securities Yawen, Hwang, Assistant Professor, Dept. of Risk Management and Insurance, Feng Chia University Hong-Chih, Huang, Associate Professor, Dept. of Risk Management and Insurance, National Chengchi University

2. 1. Introduction If you have 10 thousand dollars, you will invest these money into? BondStock v. s. The risk attitude is different with different people.

3. 1.Introduction Longevity Bond How to enhance the attractiveness of longevity bonds? Separating it. (From the idea of collateral debt obligation )

4. 1.Introduction How to price the longevity bonds? Need accurate mortality model! The purpose of this study: 1.Modifying the existing mortality models and providing a better mortality model 2.Improving the attractiveness of longevity bonds

5. 2. Literature review-mortality model Static mortality model  Gompertz (1825)  Makeham (1860)  Heligman & Pollard (1980) Dynamic mortality model  Lee-Carter (1992)  Reduction Factor Model (1860)  Logistic model (Bongaarts, 2005)  CBD model (2006)  M7 model (2009) Using two methods to modify the logistic model Considering the cohort effect, the number of parameters are unavoidable concerns.

6. 2. Literature review- securitization of mortality risk Blake & Burrows (2001) Dowd & Blake (2003) Cowley & Cummins (2005) Blake et al. (2006) Lin & Cox (2005): Wang Transformation Cairns et al. (2006): CBD model Cox et al. (2006): multivariate exponential tilting Denuit et al. (2007): Lee-Carter model

7. 2 Literature review- securitization of mortality risk In this paper, we apply the extended logistic mortality models to price longevity bonds. Furthermore, we introduce the structure of collateral debt obligation to longevity bonds. We hope to increase the purchasing appetence of longevity bonds by designing it to encompass more than one tranche. Lin & Cox (2005) Special Purpose Vehicles

8. 3.1 Logistic mortality model senescent death ratebackground death rate Thus, this model is a dynamic model. It considers the effects of age and time. Bongaarts(2005) proposes a logistic mortality model as follows: We assume the mortality rate follows Eq(1) Eq(1)

9. 3.2 Modifying methods Method I: Segment approach (from RF model)

10. 3.2 Modifying methods Method II: Background death rate might be related more reasonably to age.

11. 3.3 Mortality models

12. 3.4 Measurement Measurement 1. MAPE (Mean Absolute Percentage Error) 2. According to Lewis (1982), the standard of MAPE is described as the following table:

13. 4.1 Numerical analysis - Fitting Data: 1. USA, Japan and England & Wales: Human mortality database 2. Fitting the mortality rates of a single age range from 50-year to 89-year from 1982 to 2000.

14. 4.1 Numerical analysis - Fitting

15. 4.2 Numerical analysis - Forecasting Data: 1.Forecasting single age range from 50-year to 89-year 2.Japan, England & Wales: 2001~2006 3.USA: 2001~2005

16. 5.1 Longevity bond 5.1.1 Insurer & SPV is the survivor index. is the real survivor rate. is the payment from SPV to insurer at time t.

17. Not equivalent 5.1 Longevity bond 5.1.2 SPV & Investor If SPV pay claim to insurer, then the principal of Tranche B is decreasing at time t. The principal of Tranche A will deduct when is zero. Therefore, Tranche B is more risky than A. That is. Coupon c A Coupon c B

18. 5.1 Longevity bond Survival rate index: (Insurer) Lin & Cox (2005): Survival rate: (SPV) Modified extended logistic (beta) mortality model USA Male

19. 5.2 Numerical analysis – Static interest rate parameters

20. 5.2 Numerical analysis – Static interest rate We issue the longevity bonds (Tranche A and B) with the price at premium 20%, which is $6,500,000.

21. 5.2 Numerical analysis – Static interest rate Sensitivity analysis for SPV’s NPV Factor: premium

22. 5.2 Numerical analysis – Static interest rate Sensitivity analysis for SPV’s NPV Factor: interest rate

23. 5.3 Numerical analysis – Dynamic interest rate

24. Sensitivity analysis for SPV’s NPV

25. 6. Conclusion 1.The proposed extended logistic models performed better forecasting efficiency than the Lee-Carter and M7 model, especially the modified extended logistic (beta) model. 2.We design LBs to encompass more than one tranche. This design offers investors more choices pertaining to their different risk preferences. 3.The SPV’s NPV are influenced by interest rate and mortality rate. SPV should carefully evaluate premium and coupon rates to control their risks.

26. Q & A