Hedging European and Barrier options using stochastic optimization

We hedge European and Barrier options in a discrete time and discrete space setting by uwing stochastic optimization to minimize the mean downside hedge error under transaction costs. Scenario trees are generated using a method which ensures the absence of arbitrage and which matches the mean and variance of the underlying asset price in the sampled scenarios to those of a given distribution. The stochastic optimization based strategy is benchmarked to the method of delta hedging for the case where the underlying asset price following a discretized geometric Brownian motion and implemented for the case where the underlying asset prices is driven by a discretized Variance Gamms proces.