  We consider a semimartingale market model when the underlying diffusion has a
singular volatility matrix and compute the hedging portfolio for a given payoff
function. Recently, the representation problem for such degenerate diffusions
with respect to a minimal martingale has been completely settled. This
martingale representation and Malliavin calculus established further for the
functionals of a degenerate diffusion process constitute the basis of the
present work. Using the Clark-Hausmann-Bismut-Ocone type representation formula
derived for these functionals, we prove a version of this formula under an
equivalent martingale measure. This allows us to derive the hedging portfolio
as a solution of a system of linear equations. The uniqueness of the solution
is achieved by a projection idea that lies at the core of the martingale
representation at the first place. We demonstrate the hedging strategy as
explicitly as possible with some examples of the payoff function such as those
used in exotic options, whose value at maturity depends on the prices over the
entire time horizon.
