We consider locally risk-minimization problem when risky asset price processis described by an SDE driven by a Levy process. Our goal is to obtain an explicit representation formula for the locally risk-minimizing hedging strategy for Levy markets by using Malliavin calculus for Levy processes. Firstly, we introduce a Clark-Ocone type formula for Levy process under a change of measure. Then, we obtain an explicit representation of the Follmer-Schweizer decomposition. Moreover, we calculate Malliavin derivatives for Eupopean call options by an approximation method. Some examples including CGMY model are also discussed.
(joint work with Ryoichi Suzuki (Keio University))