Description: In December 2007, Goldman Sachs launched a product called QxX index swap, which is designed to allow market participants to hedge or gain exposure to longevity and mortality risks. This presentation offers a quantitative analysis of this brand new financial innovation. First of all, the presentation sets up a risk-neutral framework to price QxX index swaps. This framework, which is based on the dynamics of death rates under a two-factor stochastic mortality model in a risk-adjusted probability measure, yields prices [spreads] that are fairly close to the spreads that Goldman Sachs currently offers. The presentation then explores the uncertainty involved in this model-based pricing framework. Specifically, it studies parameter risk by using Markov Chain Monte Carlo [MCMC] and model risk by examining structural changes in mortality dynamics. The results indicate that both model risk and parameter risk are significant. Actuaries should therefore be aware of these issues when placing a value on a longevity index swap.

Description: In this paper, we derive three important longevity Greeks on the basis of an extended version of the Lee-Carter model that incorporates stochastic volatility.

Description: In this paper, we investigate the dynamics of the Lee-Carter mortality index parameter kt. Specifically, we perform statistical hypothesis tests to examine whether the mortality indexes for Canada, England and Wales and the United States are best described by stochastic trends difference stationary models or deterministic trends trend stationary models. The empirical results favor broken-trend stationary models over difference stationary models, which are used in most previous applications of the Lee-Carter method. The results also give strong statistical evidence that the rates of mortality decline for the three populations have significantly accelerated in mid-1970s.