Modeling parameter risk in premium risk in multi‐year internal models

Purpose – 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. Design/methodology/approach – The authors present a variety of methods for modeling parameter risk (asymptotic normality, bootstrap, Bayesian) with different statistical properties. They then integrate these different modeling approaches in an internal risk model and compare their results with those from modeling approaches that measure only process risk in premium risk. Findings – The authors 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). The authors' results also demonstrate that parameter risk substantially influences risk‐based capital and strategic management decisions, such as reinsurance. Practical implications – The authors' findings emphasize that it is necessary to integrate parameter risk in risk modeling. Their 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. Originality/value – To the authors' knowledge, there are no model approaches or studies on parameter uncertainty for projection periods of not just one, but several, accident years; however, consideration of multiple years is crucial when thinking strategically about enterprise risk management.