Static Hedges of Barrier Options Under Fast Mean-Reverting Stochastic Volatility

In this paper, we suggest a numerically stable method for static hedging of barrier options under fast mean-reverting stochastic volatility with transaction costs. We elucidate how perturbation theory converts static hedging on time–volatility grid into the problem of designing two simpler static hedges on time grid, and see why this precludes any ill-conditioned problem from springing up. Our static hedging approach is an effective means to statically replicate the barrier option, and can therefore solve the problem of transaction costs by obtaining stable weights of the portfolio. Simulation results show that our method could obtain better hedging performance compared to preceding static hedge methods.