Parameter risk in time-series mortality forecasts

The projection of mortality rates is an essential part of valuing liabilities in life-insurance portfolios and pension schemes. An important tool for risk-management and solvency purposes is a stochastic projection model for mortality. We show that ARIMA models can be better representations of mortality time-series than simple random-walk models. We also consider the sometimes-overlooked issue of parameter risk in time-series models — formulae are given for decomposing overall risk into undiversifiable trend risk (parameter uncertainty) and diversifiable volatility. Using the bootstrap approach from Pascual et al. (2004) we find that, while certain kinds of parameter risk are negligible, others are too material to ignore. In our specific mortality examples, a modification to the procedure from Pascual et al. (2004) reduced bias when bootstrapping the variance of the volatility, σ2 . The conclusions have relevance to projection models used by insurers in the European Union under Solvency II.