Modeling Parameter Risk in Premium Risk in Multi-Year Internal Models

The purpose of this paper is to illustrate the importance of modeling parameter risk in premium risk, especially when data are scarce and a multi-year projection horizon is considered. Internal risk models often integrate both process and parameter risks in modeling reserve risk, whereas parameter risk is typically omitted in premium risk, the modeling of which considers only process risk. We present a variety of methods for modeling parameter risk (asymptotic normality, bootstrap, Bayesian) with different statistical properties. We then integrate these different modeling approaches in an internal risk model and compare our results with
those from modeling approaches that measure only process risk in premium risk. We show that parameter risk is substantial, especially when a multi-year projection horizon is considered and when there is only limited historical data available for parameterization (as is often the case in practice). Our results also demonstrate that parameter risk substantially influences risk-based capital and strategic management decisions, such as reinsurance. Our findings emphasize that it is necessary to integrate parameter risk in risk modeling. Our findings are thus not only of interest to academics, but of high relevance to practitioners and
regulators working toward appropriate risk modeling in an enterprise risk management and solvency context.