Longevity risk represents a substantial threat to the stability of support programmes for the elderly, most notably to the subset that provides income protection but also to non-traditional products such as home equity release schemes.

One approach to dealing with longevity risk is to model key factors that influence mortality; this may be achieved using aggregate (causal) mortality rates or panel data with individual-specific covariates. Another approach to modelling longevity risk is via an investigation of positive quadrant dependence between lives, which requires a multivariate framework. Once this is in place, longevity risk may be investigated on various fronts ranging from entire populations to couples.

Researchers active in this area
Name	Keywords
Dr Daniel Alai	Cause-of-death mortality; home equity release products; lifetime dependence modelling; stochastic mortality modelling.
Prof Paul Sweeting	Credibility models; post-code rating; stochastic mortality modelling.
Guy Thomas	House price insurance.

Areas of research

Causal mortality modelling

There is an inherent loss of information when aggregating mortality rates by cause-of-death. Insight can be gained when studying causal mortality rates, but care needs to be taken to account for dependence.

First, intrinsic dependence is present among the causal mortality rates due to the competing nature of their relationship.

Second, extrinsic dependence may also exist, which can contribute to predict future trends; this second form is significantly more difficult to address.

However, a suitable model may provide answers to some very interesting scenario-based questions. For example What are the consequences of a cure for cancer?

Home equity release products

Guy Thomas

The reverse mortgage, perhaps the most well-known home equity release product, is a type of collateralized loan. The borrower receives a lump sum, which primarily depends on the value of their home. The loan accumulates interest and is repaid at contract termination using the sale proceeds of the home.

Contract termination may be triggered by various random events such as the death of the borrower. Should the loan balance exceed the home value at contract termination, the borrower is not liable for the excess; in other words, their liability is capped.

It is clear that longevity plays an important role in determining the parameters of such products. However, house price movements, rental yields and interest rates must also be carefully considered.

Among the work done at Kent, Guy Thomas has proposed a new type of ‘perpetual’ futures contract that could be used as a hedging instrument to limit exposure to house price fluctuations. Dr Daniel Alai has investigated contract termination probabilities in order to facilitate comparisons of various home equity release products.

If the data provides supplementary covariates, such as socioeconomic variables, further questions of significant interest to policy-makers may be posted. For example Which cause should receive the most public funding in order to reduce the life expectancy gap between the most affluent and the most deprived?

Lifetime dependence modelling

Dr Daniel Alai

Maintaining the adequacy and sustainability of income protection programmes is the goal of lifetime dependence modelling. This is motivated through the intimate link between longevity risk and positive dependence structures.

Longevity risk is systematic so it manifests itself through positive quadrant dependence (i.e. random lifetimes jointly moving in a positive direction). We quantify the presence or change in longevity risk by monitoring the presence or change in the dependence structure of lives.

A benefit of looking at longevity risk this way is that the framework allows for additional applications, such as investigating joint-lives (or groups of lives of arbitrary size).

It is important to consider an appropriate marginal distribution as well as dependence structure. The presence of truncated and censored data further complicates model calibration techniques. Algorithms using appropriate statistics must be carefully considered.

Stochastic mortality modelling

Historic mortality changes are used to not only estimate future mortality but also to determine the uncertainty in those estimates. This includes looking at different ways of assessing the “cohort effect” – the impact that an individual’s year of birth has on their expected mortality. In addition, the impact of their age and the calendar year are considered.

This analysis allows for the construction of a range of stochastic mortality models for use by pensions and insurance actuaries.

Mortality rates may also be estimated using information from individuals and from the groups to which they belong. This includes “postcode rating”, where the place of birth is used as a proxy to determine mortality risk classes.

It also includes credibility, which looks at the extent to which information from a particular group can be combined with external experience to produce a weighted estimate of future mortality rates.