Before revision:  Our representation is given in terms of Malliavin calculus for L\'evy processes .
After revision:  Some representations of mean-variance hedging strategies for jump type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin calculus for L\'evy processes .