In this article, we consider the evolution of the post-age-60 mortality curve in the United Kingdom and its impact on the pricing of the risk associated with aggregate mortality improvements over time: so-called longevity risk. We introduce a two-factor stochastic model for the development of this curve through time. The first factor affects mortality-rate dynamics at all ages in the same way, whereas the second factor affects mortality-rate dynamics at higher ages much more than at lower ages. The article then examines the pricing of longevity bonds with different terms to maturity referenced to different cohorts. We find that longevity risk over relatively short time horizons is very low, but at horizons in excess of ten years it begins to pick up very rapidly.A key component of the article is the proposal and development of a method for calculating the market risk-adjusted price of a longevity bond. The proposed adjustment includes not just an allowance for the underlying stochastic mortality, but also makes an allowance for parameter risk. We utilize the pricing information contained in the November 2004 European Investment Bank longevity bond to make inferences about the likely market prices of the risks in the model. Based on these, we investigate how future issues might be priced to ensure an absence of arbitrage between bonds with different characteristics.

We compare quantitatively eight stochastic models explaining improvements in mortality rates in England and Wales and in the United States. On the basis of the Bayes Information Criterion (BIC), we find that, for higher ages, an extension of the Cairns-Blake-Dowd (CBD) model that incorporates a cohort effect fits the England and Wales males data best, while for U.S. males data, the Renshaw and Haberman (RH) extension to the Lee and Carter model that also allows for a cohort effect provides the best fit. However, we identify problems with the robustness of parameter estimates under the RH model, calling into question its suitability for forecasting. A different extension to the CBD model that allows not only for a cohort effect, but also for a quadratic age effect, while ranking below the other models in terms of the BIC, exhibits parameter stability across different time periods for both datasets. This model also shows, for both datasets, that there have been approximately linear improvements over time in mortality rates at all ages, but that the improvements have been greater at lower ages than at higher ages, and that there are significant cohort effects.

No abstract

We investigate asset-allocation strategies open to members of defined-contribution pension plans with a model that incorporates asset, salary (labour-income) and interest-rate risk. We propose a novel form of terminal utility function, incorporating habit formation, that uses the member's final salary as a numeraire. The paper discusses various properties and characteristics of the optimal asset-allocation strategy both with and without the presence of non-hedgeable salary risk. Finally, we compare the performance of the optimal strategy with some popular alternatives used by pension providers and we conclude that it significantly enhances the welfare of a wide range of potential plan members relative to these other strategies. r

One of the key problems facing annuity providers is mortality risk, the risk of underestimating mortality improvements. The authors argue that the government could help the issuers of annuities to hedge aggregate mortality risk by introducing a new type of bond, which the authors call a survivor bond. The future coupons on this bond depend on the percentage of the population of retirement age on the issue date who are still alive on the future coupon payment dates. The coupons on the bond therefore decline over time but continue in payment until the last members of this population cohort have died. The government would therefore be assuming a risk that has hitherto been borne by the private sector. However, governments now issue inflation-indexed bonds, and the authors would argue that inflation risk is a much greater risk than mortality risk in aggregate. Furthermore, governments directly contribute to mortality risk: for example, they promote public health campaigns that, if successful, lead to mortality improvements that are difficult to predict many years ahead. Survivor bonds enable pension provision to be a shared responsibility between the public and private sectors.