Impact of Model Misspecification on the Value-at-Risk of Unimodal T-Symmetric Distributions

This article assesses the impact of model uncertainty on Value-at-Risk calculations. We assume that the true, yet unknown, model possesses certain qualitative properties, such as unimodality and symmetry, possibly after a concave transformation (e.g., log-symmetry). Additionally, we consider available information on the median, interpercentile range, and moments. We then derive the maximum possible Value-at-Risk for a model that adheres to this available information. This article provides a method to measure potential errors when using Value-at-Risk with misspecified loss models. As a result, financial and actuarial decision makers can gain a better understanding of model uncertainties and the dynamics of model outcomes, leading to better-informed decisions. Moreover, this article assists banks and insurance companies in allocating the right amount of reserves necessary to address model risk, thus reducing the need for excessive conservatism.