PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

WHEN CAN ACCIDENT YEARS BE REGARDED AS DEVELOPMENT YEARS? 249Consider the issue of accident years being treated like developmentyears. Imagine you have homogeneous accidentyears (a not uncommon occurrence, especially after you adjustfor changes in exposure and inflation, assuming no superimposedinflation). You wouldn’t predict the level of thenext accident year using ratios–it would be far more sensibleand informative to take some kind of average. But aswe have seen, the chain ladder does use ratios in both directions.If this way of looking at the chain ladder seems a little nonsensical,it is because we are inferring additional meaning in theusual form of the chain ladder that it doesn’t really possess. Thetwo descriptions (the across version and the down version) arein reality the same description of the data.Note also that we can now see that there are in fact parametersin both directions in the chain ladder. This is not a consequenceof any particular formulation of the chain ladder–every chain-ladder-reproducing model has degrees of freedomto fit the data (i.e., parameters) that run both across anddown. Some formulations make the existence of both kindsof parameters explicit (as in Renshaw and Verrall [8]); someother formulations do not (such as Mack [6])–the row parametersbecome hidden by the fact that the model is conditionedon the first column. The chain ladder itself still unavoidablyhas degrees of freedom to fit changes in accidentlevel, so the parameters remain, even where not explicitly representedin the formulation. All formulations of the chain ladderhave 2s ¡ 1 parameters for the mean, though the numberof variance parameters and distributional assumptions mayvary.We note that so many parameters make the forecasts quitesensitive to relatively small changes in a few values, making thechain ladder unsuitable for forecasting. Yet even with so manyparameters the chain ladder is still unable to model changingsuperimposed inflation.