Identifying and Quantifying the Cost Drivers of Loss Development: A Bridge Between the Chain Ladder and Statistical Modeling Methods of Loss Development
The analysis presented in this paper reflects NCCI's ongoing commitment to developing techniques and processes that enhance our methodologies. Recent examples include introducing a new approach to class ratemaking, remapping of hazard groups, changing the treatment of large losses, and developing statistical models for estimating loss trends. This paper addresses recent work at NCCI on enhancing the modeling of loss development.
The Critical Role of Estimating Loss Development
An estimate of ultimate claims costs is essential to setting loss reserves and in determining trends in loss costs, which is a key factor in ratemaking. At its most basic level, this requires some method of estimating future payments on claims from past underwriting periods. In general, it seems appropriate to analyze the observed year-to-year growth in losses of prior underwriting years to estimate how claims costs of more recent years might be expected to evolve. This typically is referred to as "loss development."
The most popular actuarial methods for evaluating and projecting loss development are largely a blend of mechanical and subjective analyses. A leading example is the chain ladder method applied to a loss triangle. The chain ladder method calculates period-to-period rates of growth in reported cumulative losses―typically either cumulative payments or cumulative paid plus case reserves―by underwriting period. These growth rates for a given report period are averaged for various combinations of underwriting periods; actuarial judgment is then used to select a set of development factors deemed to be most representative of the anticipated pattern of future loss development. The selected development factors are then applied to the most recent reported cumulative losses for each open underwriting period to forecast future remaining claim payments and, hence, total ("ultimate") losses for each underwriting period.
Interest is growing in the use of statistical models to estimate ultimate losses. In particular, the models developed by Barnett and Zehnwirth and by Schmid have garnered the most attention recently. The two models share a common framework but rely on markedly different statistical techniques to analyze claims experience. The common framework characterizes loss development in terms of three time dimensions:
- Calendar year
- Development year
- Exposure or underwriting year