Longevity risk modelling with application to insurer longevity risk based capital stress margins

Abstract

Future mortality rates are uncertain and the risk that estimated mortality rates will be higher than observed rates has negative financial implications for providers of living benefit ts including life annuities and pensions. This thesis studies time trends and cohort trends in mortality rates to determine the number of factors that drive mortality changes. An econometric analysis of mortality improvements is used to give a clearer picture of the stochastic nature of mortality rates in a lower dimensional data space as this thesis uses co integration analysis for dimension reduction.A multi-country analysis of standardized mortality rates fi nds evidence of stochastic trends and a signifi cant number of common factors. However, no evidence of common stochastic trends is found. An analysis of Australian mortality rates establishes there are non-stationary and stationary mortality rates by age. The common stochastic trends across age-groups which are exhibited within the Australian data lead to the characterization of mortality rates using a stochastic trend model. Dimension reduction is performed using the Heligman and Pollard (1980) parametric mortality model. The trends in the data are reflected using flexible Vector Autoregressive (VAR) models allowing for correlation between the estimated Heligman and Pollard model parameters. Bayesian Vector Autoregressive (BVAR) models which additionally quantify parameter risk are shown to signifi cantly improve the forecast accuracy when fi tting the developed HP-BVAR model to data from 1946-1995 and then comparing its out-of-sample forecasts to observed data from 1996-2007 for Australian mortality rates. Allowing for parameter uncertainty shows it to be a signi cant component of total risk since the results are realistic probabilistic forecasts. The HP-BVAR model is applied to the calibration of the longevity stress margin of the life insurance capital charge. The structure and magnitude of the current simpli fication by APRA result in a longevity stress margin that is found to be too prudent and too generalised. An alternative age-dependent simpli fication is proposed.