Comment on “Mortality-Indexed Annuities: Avoiding Unwanted Risk” Jack C. Yue National Chengchi University September 26, 2009

About the paper “Mortality-Indexed Annuities: Avoiding Unwanted Risk”  By A. Richter and F. Weber This is an interesting paper and I will focus on the following two questions:  Practical issues  Comments on Simulation

Longevity Risk This paper provides an interesting summary of the longevity risk, including its history.  Using stochastic methods to model mortality seems to be a popular choice for handling longevity (systematic) risk. Two major concerns in applying these models: model uncertainty and parameter uncertainty.  The authors also discuss the possible risks for the insurers and policyholders.

Mortality-Indexed Annuities The authors proposed mortality-indexed annuities and the benefit of policyholders depends on actual mortality experience.  The policyholders bear the longevity risk. There are two questions about the products:  Marketability (e.g., Catastrophe Mortality Bond by Swiss Re)  Competitiveness (e.g., compete with conventional annuities)

Mortality-Indexed Annuities (conti.) Since the mortality rates are small in the accumulation phase, the focus shall be on the payout phase.  The nature of mortality-indexed annuities shall be similar to variable annuities, instead of unit- linked annuities.  The mortality improvement plays an important role and the benefit would have large variation if the size of policyholders is small.

Practical Concerns A group of homogeneous policyholders is needed (e.g., l x persons at time t = 0).  What size of the group would be adequate? (small size incurs large variance at older ages)  Policy needs to start at the same time?  Different annuity unit purchased?  Different investment strategies (e.g., variable annuities)

Computer Simulation The authors use computer simulation to compare the mortality-indexed annuities with the conventional annuities.

Suggestions about Simulation In addition to the values provided by the authors, it would be more beneficial if the probability that the benefit is lower than a certain value is given.  e.g., Pr.(80% original benefit) Also, it would be helpful to study the relationship of group size and the probability.

Suggestions about Simulation (cont.) The longevity risk is a systematic risk, caused by higher than expected reduction in mortality. The MIB switches the risk to the policyholders and we want to know what is the catch to them.  e.g., Sensitivity Analysis of the mortality rates (say, the parameter  t in the Lee-Carter model is 10% or 20% larger in slope).  If possible, calculate the result including both the mean shift and variance.

Thank you for your attention!