Generalized Linear Models in life insurance: Decrements and risk factor analysis under Solvency II

Insurers will generally want accurate knowledge of recent lapse, surrender and mortality (collectively termed ‘decrements’ for the purposes of this abstract) rates for pricing, statutory reserving, Embedded Value estimation and Economic Capital calculations. Some of these applications require ‘best estimate’ parameters, while others require prudent parameters; in both cases, however, it is important to know as accurately as possible the underlying reality. The Solvency II draft directive and the CFO Principles explicitly require an investigation of the correlation of policyholder behaviour, such as surrender rates, with other risk factors affecting the insurance entity, such as market risks. Generalised linear models (“GLMs”) provide a powerful statistical analytic tool to investigate the underlying reality of the investigated parameter in a way that can also give information on how economic conditions may have affected observed policyholder behaviour. Furthermore, such analyses allow better understanding of the likely variability in the decrement rates for the purpose of generating relevant sensitivity tests and calibrating internal models in so far as the stochastic modelling of longevity and mortality risk is concerned. Traditional analytic techniques are of little use in this context, for various reasons. Correlations in the data between factors of interest will make one-way analyses of those factors incorrect. For instance, a traditional analysis will not be able to analyse at the same time age and policy duration. Insurers would normally expect to find correlations between the following factors within any one product class: policy duration, age, amount of benefit, sex. Because traditional analyses fail to take due account of the correlation between benefit amount and other factors, the effect of benefit amount on decrement probability will not be measured correctly. The traditional approach of weighting by benefit amount takes some account of amount, but in an incorrect way. In a cash flow projection, whether used in product pricing or portfolio projections (financial reporting), the main driver is not in fact the lives or policies themselves but the benefit amounts, and it is therefore vital to model correctly the effect of benefit amount: a ‘high benefit amount, low off rates’ projection will give substantially different (and more accurate) results than a projection based on ‘average across amounts’ decrement rates. Furthermore, traditional analyses are also restricted by concerns about time trends in the data: it is not generally considered ‘safe’ to use more than three-four years of data, especially for the mortality decrement. Generalised linear models (“GLMs”) provide a relatively simple and robust way to analyse the effect of many different factors on some observed event. For instance, the effect of policyholder age, benefit amount and duration on decrement rates within a particular product class can be measured. GLMs will take account automatically of all correlations in the data. This powerful aspect of such models entails many advantages: Age and duration can be analysed together, giving useful information on a generally disregarded aspect of decrement experience. The amount of the benefit can be used as a factor in the model, allowing the high/low amount decrement differential to be correctly measured and hence substantially improving the accuracy of cash flow projections. Calendar year of exposure can be used as a factor, allowing the use of many years of data. This will both improve the robustness of the results, and provide more information about trends that may be of use in informing subsequent thinking about likely trends. This is particularly useful in the context of the mortality decrement, and may also help to investigate the effect of economic conditions on the lapse/surrender decrements. GLMs also provide the ability to analyse ‘interactions’ between factors: for instance, how the duration effect might differ between high/medium/low benefit amount groups, or between different distribution channels. The aim of this paper is to show, using real-life case studies where possible, how GLMs can provide financial services institutions with more accurate estimates of observed decrement experience, and how these analyses can be of particular value in understanding likely future trends and in informing dynamic lapse risk / market risk modeling, an area that is becoming increasingly important in the context of the European Solvency II project.