The Common Shock Model for Correlated Insurance Losses

Abstract

This paper discusses an approach to the correlation problem in which losses from different lines of insurance are linked by a common variation (or shock) in the parameters of each line's loss model. The paper begins with a simple common shock model and graphically illustrates the effect of the magnitude of the shocks on correlation. Next it describes some more general common shock models that involve common shocks to both the claim count and claim severity distributions. It derives formulas for the correlation between lines of insurance in terms of the magnitude of the common shocks and the parameters of the underlying claim count and claim severity distributions. Finally, it shows how to estimate the magnitude of the common shocks. A feature of this estimation is that it uses the data from several insurers.