Auto-static for the people: risk-minimizing hedges of barrier options

We present and test a method for computing risk-minimizing static hedge strategies. The method is straightforward, yet flexible with respect to the type of contingent claim being hedged, the underlying asset dynamics, and the choice of risk-measure and hedge instruments. Extensive numerical comparisons for barrier options in a model with stochastic volatility and jumps show that the resulting hedges outperform previous suggestions in the literature. We also demonstrate that the risk-minimizing static hedges work in an infinite intensity Levy-driven model, and a number of controlled experiments illustrate that hedge performance is robust to model risk.