Model Risk of Contingent Claims

Abstract

Paralleling regulatory developments, we devise value-at-risk and expected shortfall type risk measures for the potential losses arising from using misspecified models when pricing and hedging contingent claims. Essentially, losses from model risk correspond to losses realized on a perfectly hedged position. Model uncertainty is expressed by a set of pricing models, relative to which potential losses are determined. Using market data, a unified loss distribution is attained by weighing models according to a relative likelihood criterion. Examples demonstrate the magnitude of model risk and corresponding capital buffers necessary to sufficiently protect trading book positions against unexpected losses from model risk.

Keywords: model risk, parameter uncertainty, hedge error, value-at-risk, expected shortfall

JEL Classification: G32, G13