Pricing Stochastic Barrier Options in Presence of Jumps

We consider the problem of hedging a contingent claim, in a market where prices of traded assets can undergo jumps, by trading in the underlying asset and a set of traded options. We give a general expression for the hedging strategy which minimizes the variance of the hedging error, in terms of integral representations of the options involved. This formula is then applied to compute hedge ratios for common options in various models with jumps, leading to easily computable expressions. The performance of these hedging strategies is assessed through numerical experiments