Before revision: We apply the quadratic hedging scheme developed by F\"ollmer , Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process . The main contributions of this work consist of showing that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure is only available in the presence of bounded innovations.
After revision: We apply the quadratic hedging scheme developed by F\"ollmer , Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process and show that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure is only available in the presence of bounded innovations.