Annuity Product Valuation and Risk Measurement under Correlated Financial and Longevity Risks

Longevity risk is a non-diversifiable risk and regarded as a pressing socio-economic challenge of the century. Its accurate assessment and quantification is therefore critical to enable pension-fund companies provide sustainable old-age security and maintain a resilient global insurance market. Fluctuations and a decreasing trend in mortality rates, which give rise to longevity risk, as well as the uncertainty in interest-rate dynamics constitute the two fundamental determinants in pricing and risk management of longevity-dependent products. We also note that historical data reveal some evidence of strong correlation between mortality and interest rates and must be taken into account when modelling their joint dynamics. In this thesis, we model and examine the impact of nonlinearity and correlation on an annuity product. A regime-switching approach to address nonlinearity is embedded both in the Lee-Carter model for mortality rate modelling and prediction, and in the Vasicek model for capturing interest-rate movements. In the valuation and computation of risk measures for an annuity that are being carried out to satisfy regulatory requirements, the correlation structure between mortality and financial risks is explicitly modelled. Our proposed modelling framework is implemented on simulated data as well as actual data covering the South Korean population and Korean bond yields for the period 1980-2015. Our results demonstrate the significant effect of correlation on annuity and risk-metric values. Finally, we found that the use of regime-switching techniques for both mortality and interest rate modelling creates a greater latitude in obtaining accurate prices, based on models’ parameter estimates, and in setting capital adequacy that avoids substantial over-reserving or under-reserving.