When pricing and hedging a derivative, we face model risk, that is, the risk of choosing the wrong dynamics for the financial market. A widely recognized framework for model risk was proposed in (Cont, 2006). The paper states axioms any measure of model risk should fulfill. Any measure of model risk is based on a class of possible measures, which represents the uncertainty on the specification of probabilities. A mapping is developed that fulfills the axioms and assigns each payoff a monetary value that represents its model risk. In a specific example, this mapping is based on the price range of a payoff within the model class. We define model risk based on the value difference of the hedge portfolio when this evaluates under different measures. Based on the hedge error between two different measures we derive a distribution of the hedge error on the entire model set. As a capital charge we use an average Value at Risk approach. We show how the hedge based measure relates to the measure proposed in (Cont, 2006).
R. Cont. Model uncertainty and its impact on the pricing of derivative instruments. Mathematical Finance, 16(3):519-547, 2006.