Abstract
We introduce a simple extension to the CBDX model to project cohort mortality rates to extreme old age. The proposed approach fits a polynomial to a sample of age effects, uses the fitted polynomial to project the age effects to ages beyond the sample age range, then splices the sample and projected age effects, and uses the spliced age effects to obtain mortality rates for the higher ages. The proposed approach can be used to value financial instruments such as life annuities that depend on projections of extreme old age mortality rates.
Highlights
The CBDX model (Dowd et al, 2020 [1]) was recently introduced as a workhorse mortality model for the adult age range
Appendix A sets out the relationships between age effects, death rates, and mortality rates
Projecting Mortality to Extreme Old Age with the CBDX Model: An Empirical where c t −Based x refers the year of birth; α x, κ t, and γ c are the age-related
Summary
The CBDX model (Dowd et al, 2020 [1]) was recently introduced as a workhorse mortality model for the adult age range (i.e., excluding the accident hump and younger ages). The original CBD models were designed for higher ages As they have no age-related SVs, the models can be used to project mortality rates to any age without being constrained by the range of ages in the sample data used to calibrate the age effects. We consider how the CBDX model can be used to project mortality rates beyond the upper end of the age range over which the model was estimated, allowing model users to project mortality rates out to extreme old age. This is important, for example, for a life insurer wishing to price a life annuity or sell an equity release mortgage. Appendix A sets out the relationships between age effects, death rates, and mortality rates
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