It is very important for an insurer to understand its portfolios of business and the assumptions underlying them. Furthermore, in the Solvency II world that we are about to enter, insurers will be required to demonstrate their validation of material assumptions.
Mortality is an example of what is likely to be a material assumption. When an actuary values any type of insurance policy contingent on the life or death of the policyholder, they need to estimate the policyholder’s mortality now and at future ages.
Understanding the sensitivity of the liabilities to the mortality assumption and key ages is helpful to actuaries as it can focus their attention, analysis and validation efforts on the assumptions that have the biggest impact on liability values.
Wait… ‘sensitivities’? ‘key ages’?
We define the ‘sensitivity’ to the change in mortality at a particular age as the percentage change in the liability as a result of changing the mortality assumptions at a single age and keeping other ages unchanged.
The ‘key age’ for mortality rates is then the age at which the sensitivity is highest.
Case study – annuities
The sensitivity of annuity type liabilities to mortality at various ages is a product of:
- The base mortality rate – if it is already high, then the liabilities will be more sensitive to changes in it.
- The expected outstanding term of the annuity – the longer the remaining liability, the more sensitive it is likely to be.
We can think of this product as the age at which part of the liability ‘dies’. The sensitivity is higher at intermediate ages and lower both at younger ages (where the mortality rate is low) and at older ages (where the remaining liability is low).
Our analysis suggests that the key age for mortality rates, for ‘typical’ annuities, is in the region of 85 to 90. For this hypothetical product, an actuary may want to consider focusing more of their validation efforts to this key age range. There are many ways that this could be done. For example, if data permits, a detailed experience analysis could be done into the key age range or if not, the assumption could be validated against alternative datasets – perhaps by looking at the underlying data sources in addition to published tables.