Back-Testing the ODP Bootstrap of the Paid Chain-Ladder Model with Actual Historical Claims Data

This paper back-tests the popular over-dispersed Poisson bootstrap of the paid chain-ladder model from England and Verrall(2002), using data from hundreds of U.S. companies, spanning three decades. The results show that the modeled distributions underestimate reserve risk. We investigate why this may occur, and propose two methods to increase the variability of the distribution to pass the back-test. In the first method, we use a set of benchmark systemic risk distributions. In the second method, we show how to apply a Wang transform to estimate the systemic bias of the chain-ladder method over the course of the underwriting cycle.