1. Longevity Risk, Rare Event Premia and Securitization 08/06/2007 ARIA Annual Meeting 2007 Longevity Risk, Rare Event Premia and Securitization By Yijia Lin and Samuel H. Cox Discussion by Nadine Gatzert, University of St. Gallen

2. Longevity Risk, Rare Event Premia and Securitization 08/06/2007 Summary 2   Motivation - -Management of longevity risk very important (increasing future annuity demand) - -Insurance-linked securitization (increase underwriting capacity by offloading the risk on capital markets) - -EIB longevity bond: hedge long-term systematic longevity risk, intended for pension plans - -Problematic design: too expensive, covers entire annuity payment (ground-up protection) - -Alternative design: cover payments of survivors in excess of strike level (extreme risk protection, longevity call option) based on population longevity index (public data, reduces moral hazard)

3. Longevity Risk, Rare Event Premia and Securitization 08/06/2007 Summary   Mortality dynamics - -Combination of geometric Brownian motion and compound Poisson process, calibrate model to US population longevity index   Pricing model - -Liu/Pan/Wang (2005): take into account imprecise knowledge about rare longevity events - -Equilibrium security premium (total risk premium): - -Risk aversion (  ) => diffusion risk premium; jump-risk premium, - -Model uncertainty aversion (  ) => rare-event premium 3

4. Longevity Risk, Rare Event Premia and Securitization 08/06/2007 Comments 4   General comments - -Topic of relevance, paper is well-motivated - i -Longevity call option: interesting design - -Application of Liu/Pan/Wang (2005)-model to pricing longevity risks is new (introduction of rare-event premium) - -Model can explain high risk premium of securities linked to catastrophe risks due to rare-event premium

5. Longevity Risk, Rare Event Premia and Securitization 08/06/2007 Comments   Further analysis and extensions - -How do you actually estimate / fix the model risk aversion parameter  when pricing a longevity option? - -Estimation of jump parameters difficult (now: 1974 – 1977 due to significant mortality improvement, 231% higher than 1946-2003) - -Calibrate model to other data, use different mortality indices (different countries) - -Effect on call option price when varying strike level, time-to-maturity, different age cohort - -Pricing model: apply alternative utility specifications (see Liu/Pan/Wang, 2005) 5