Model risk quantification based on relative entropy

Daniel Arrieta

Abstract

Model risk can be broadly defined as the possibility of suffering losses due to errors either in the development or use of models. Financial pricing and risk measurement are subject to model risk, and its quantification is a hot topic in both academia and the financial industry. This paper presents a technique for challenging derivative pricing models that will also help to quantify model risk. The proposed approach is based on the fundamental theorems of asset pricing, which allow a model to be interpreted as a pricing measure, and on the use of the minimum relative entropy technique as a way of changing between measures. This paper makes three contributions to the literature. First, it overcomes many of the limitations of previous approaches that identified models and probability measures. Second, a statistical divergence is defined for both quantifying the divergence between measures, and therefore between models, and determining the set of optimal market instruments in the calibration of models. Third, the proposed methodology is able to assess the model risk of a target portfolio. Further, it is theoretically possible to determine a model without model risk for such a portfolio. This last framework has been explicitly designed to be easily applied by financial industry practitioners.