An Extension to the Cape-Cod Method with Credibility Weighted Smoothing

The Cape Cod method is a commonly used technique where the a priori loss ratio is calculated as the weighted average of the chain ladder ultimate loss ratios across all years with the “used” premium as the weights. It applies the same a priori loss ratio estimate (on a trended, current rates level) across all years, without consideration for any possible changes that may have occurred. A difficulty arises when the loss ratios show improvement or deterioration, which is a fairly common scenario. When this occurs, the amount of credibility that should be given to the shift is mostly left to guesswork.

This paper uses the Kalman filter to automatically smooth the loss ratios based on the amount of credibility inherent in the data in a manner that is robust and that is consistent with the Cape Cod method. It is shown how this method can be thought of as a credibility weighting between the Cape Cod and Chain Ladder techniques, each of which are possible at the two extremes. It is then shown how external predictive information, such as the state of the economy or the insurance cycle, can be incorporated to help produce more accurate results. Simulation results are presented that illustrate the error reduction this method can provide to both historical years and to the latest year.

Keywords: Loss Reserving, Credibility, Smoothing, Kalman Filter, Trend