Risk-Minimizing Static Hedges of Barrier Options

Johannes Sivén

Centre for Mathematical Sciences
Mathematical Statistics
Lund University,

ISSN 1404-028X
We present a method for computing risk-minimizing static hedge strategies (Paper A). The method is straightforward, yet flexible with respect to the type of contingent claim being hedged, the choice of risk-measure, and the underlying asset dynamics.Experimental investigations for barrier options show that in a stochastic volatility model with jumps the resulting hedges
outperform previous suggestions in the literature. We also illustrate that the risk-minimizing static hedges work in an infinite intensity Levy-driven model, and that the performance of the hedges is robust to model risk. In Paper B we extend the method and fill a hole in the literature by investigating static hedging of barrier options with plain vanilla in the presence of realistic bid/ask spreads. Spreads for options are much larger than for the underlying, and this levels the playing field in relation to traditional dynamic hedging. However, hedging with options is still the best way to reduce the risk of large losses.