Model Uncertainty and its Impact on the Pricing of Derivative Instruments
Finance Concepts Working Paper FC-04-02
35 Pages Posted: 9 Jul 2004
Date Written: June 2004
Uncertainty on the choice of an option pricing model can lead to "model risk" in the valuation of portfolios of options. After discussing some properties which a quantitative measure of model uncertainty should verify in order to be useful and relevant in the context of risk management of derivative instruments, we introduce a quantitative framework for measuring model uncertainty in the context of derivative pricing. Two methods are proposed: the first method is based on a coherent risk measure compatible with market prices of derivatives, while the second method is based on a convex risk measure. Our measures of model risk lead to a premium for model uncertainty which is comparable to other risk measures and compatible with observations of market prices of a set of benchmark derivatives. Finally, we discuss some implications for the management of "model risk."
Keywords: model uncertainty, Knightian uncertainty, option pricing, model risk, coherent risk measures, convex risk measures
JEL Classification: G13
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