Chain Ladder Under Aggregation of Calendar Periods

The chain ladder model is defined by a set of assumptions about the claim array to which it is applied. It is, in practice, applied to claim arrays whose data relate to different frequencies, e.g., yearly, quarterly, monthly, weekly, etc. There is sometimes a tacit assumption that one can shift between these frequencies at will, and that the model will remain applicable. It is not obvious that this is the case. One needs to check whether a model whose assumptions hold for annual data will continue to hold for a quarterly (for example) representation of the same data. The present paper studies this question in the case of preservation of calendar periods, i.e., (in the example) annual calendar periods are dissected into quarters. The study covers the two most common forms of chain ladder model, namely the Tweedie chain ladder and Mack chain ladder. The conclusion is broadly, if not absolutely, negative. Certain parameter sets can indeed be found for which the chain ladder structure is maintained under a change in data frequency. However, while it may be technically possible to maintain the chain ladder model under such a change to the data, it is not possible in any reasonable, practical sense.