A Value-at-Risk framework for longevity trend risk

Longevity risk faced by annuity portfolios and defined-benefit pension schemes is typically long-term, i.e. the risk is of an adverse trend which unfolds over a long period of time. However, there are circumstances when it is useful to know by how much expectations of future mortality rates might change over a single year. Such an approach lies at the heart of the one-year, value-at-risk view of reserves, and also for the pending Solvency II regime for insurers in the European Union. This paper describes a framework for determining how much a longevity liability might change based on new information over the course of one year. It is a general framework and can accommodate a wide choice of stochastic projection models, thus allowing the user to explore the importance of model risk. A further benefit of the framework is that it also provides a robustness test for projection models, which is useful in selecting an internal model for management purposes.