A practical guide to measuring reserve variability using: bootstrapping, operational time and a distribution-free approach

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The purpose of this paper is to describe some of the practical steps that are involved in various ways of measuring reserve variability. It is aimed at those who have been tempted by the theory but have been put off by the lack of explicit details of what on earth you do in practice! The three methods described are Bootstrapping, Operational Time and Thomas Mack's Distribution-free approach. The first two of these methods were described in a 1993 Working Party paper on Variance in Claim Reserving. Following that paper, various people expressed an interest in trying out some of the techniques, but stumbled at translating theory into practice. This stumbling was the prompt for this paper to be written. It is not the intention to go into the theoretical considerations of the various methods in any great detail. For further information regarding Bootstrapping and Operational Time, the reader is referred to the 1993 Working Party Paper on 'Variance in Claim Reserving'. Thomas Mack's Distribution-free approach is described in his prizewinning CAS paper 'Measuring the Variability of Chain Ladder Reserve Estimates'. Details of all three methods may be obtained from the various sources listed in the bibliography. The 1993 Working Party Paper compared the results from a variety of stochastic reserving methods as applied to three sets of real data. This work has been extended in this paper to include Thomas Mack's Distribution-free approach. The results of various different measures of variability are then compared (Bootstrapping, Operational Time, Distribution-free approach and Log-Linear Regression), to see how consistent they are in producing variability measures.