Static hedging and model risk for barrier options

Abstract

We investigate how sensitive dieren t dynamic and static hedge strategies for barrier options are to model risk. We nd that using plain vanilla options to hedge oers considerable improvements over usual -hedges. Further, we show that the hedge portfolios involving options are relatively more sensitive to model risk, but that the degree of misspecication sensitivity is robust across commonly used models. Models may produce similar plain vanilla option prices, yet give markedly dieren t prices of barrier options. This in documented for instance in Hirsa, Courtadon & Madan (2002). We investigate the natural next question: How does this aect hedge portfolios? The question is particularly interesting because there are several alternatives to traditional dynamic hedging. We look at static hedges that are portfolios of plain vanilla options constructed such that no dynamic trading is necessary to achieve replication of the barrier option. It has been argued 1 that this use of more natural hedge instruments reduces sensitivity to misspecication of model dynamics; model risk. However, most constructions of the static hedge portfolios hinge strongly on either the Black/Scholes model or a zero drift assumption, so the net eect of model misspecication is not obvious. We carry out a simulation study of the performance of hedge strategies { static and dynamic, Black/Scholes-based and market data adjusted { against dieren t classes of nonBlack/Scholes models. As many others, we nd that the use of plain vanilla options to hedge barrier options oers considerable improvements over traditional dynamic -hedging in a Black/Scholes framework. We show that this result also holds under model misspecication. Further we demonstrate that hedges involving options are relatively more model risk sensitive, and that adjustments to reect either the theoretical model structure or market