Description: Traditional pension mathematics assumes that mortality rates are fixed at a valuation date. If mortality rates reduce after a valuation date, the liabilities of a defined benefit plans 'DB plans' increase, leading to deficits. Such deficits are somewhat unpredictable, because the evolution of mortality rates is a random process. This problem, which is often called longevity risk, makes the maintenance of DB plans difficult. The International Accounting Standards Board 'IASB' has plans to tackle the arduous problem of how to disclose longevity risk on financial statements. The IASB was established in 2001 to create universal accounting standards, called International Accounting Reporting Standards 'IFRSs'. A primary objective of this paper is to propose a number of methods that can help actuaries and plan sponsors quantify and disclose longevity risk.

Description: This report documents modeling work and compares the decomposition results from the two routes described in Volume 1.

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: This report compares and contrasts methodologies for allocating U.S. historical gender-specific mortality improvement experience into four components.

Description: A detailed statistical analysis of mortality improvement for the Canadian population and for the Canadian insured lives conducted by the Institute for Quantitative Finance and Insurance.

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.

Description: Paper discusses the possible effect of outliers on the mortality index from the Lee-Carter Model. From 2005 Living to 100 and Beyond Monograph, M-LI05-1.