Abstract

Every model presents an approximation of reality and thus modeling inevitably implies model risk. We quantify model risk in a non-parametric way, i.e., in terms of the divergence from a so-called nominal model. Worst-case risk is defined as the maximal risk among all models within a given divergence ball. We derive several new results on how different divergence measures affect the worst case in heavy-tailed applications. Moreover, we present a novel, empirical way for choosing the radius of the divergence ball around the nominal model, i.e., for calibrating the amount of model risk. For heavy-tailed risks, the simulation of the worst case distribution is numerically intricate. We present an SMC (Sequential Monte Carlo) algorithm which is suitable for this task. An extended practical example, assessing the robustness of a hedging strategy, illustrates our approach. (joint work with Judith Schneider).