Quantification of model risk in quadratic hedging in finance

Abstract

In this paper the effect of the choice of the model on partial hedging in incompletemarkets in finance is estimated. In fact we compare the quadratic hedging strategies in a martingale setting for a claim when two models for the underlying stock price are considered. The first model is a geometric Lévy process in which the small jumps might have infinite activity. The second model is a geometric Lévy process where the small jumps are replaced by a Brownianmotion which is appropriately scaled. The hedging strategies are related to solutions of backward stochastic differential equations with jumps which are driven by a Brownian motion and a Poisson random measure. We use this relation to prove that the strategies are robust towards the choice of the model for the market prices and to estimate the model risk.