Risk measurement and pricing of financial positions are based on modeling assumptions, which are common assumptions on the probability distribution of the position’s outcomes. We associate a model with a probability measure and investigate model risk by considering a model space. First, we incorporate model risk into market risk measures by introducing model weighted and superposed market risk measures. Second, we quantify model risk itself and propose axioms for model risk measures. We introduce superposed model risk measures that quantify model risk relative to a reference model, which is the financial institution’s model of choice. Several risk measures that we propose require a probability distribution on the model space, which can be obtained from data by applying Bayesian analysis. Examples and a case study illustrate our approaches.

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