Model Risk: A Conceptual Framework for Risk Measurement and Hedging

Abstract

The vast majority of approaches to risk management, hedging, or portfolio planning assume that some model is given. However, under model risk, the true data generating process is not known. The focus of this paper is on problems related to the hedging of derivative contracts. We explain the main general concepts, provide economic interpretations, and illustrate our arguments by simple and straightforward examples.

Model risk can be dealt with in several ways, e.g. by not taking model risk into account at all ('naive' approach), by relying on worst case approaches, or by using Bayesian techniques. The integration of market risk and model risk turns out be crucial, since a risk measure that is used to find an optimal, risk-minimizing hedging strategy should capture the overall gains and losses of a position, irrespective of their reason. Since the full problem may be much too complicated to solve in realistic model setups, we furthermore discuss robust hedging strategies determined under simplifying assumptions. Our examples show that model risk is relevant and that the choice of risk measure matters, so that it should be based on sound economic arguments.

Keywords: Model Risk, Risk Measures, Hedging, Expected Shortfall, Bayesian statistics

JEL Classification: G12, G13