The thesis uses Malliavin’s Stochastic Calculus of Variations to identify the hedging strategies for Barrier style derived securities. The thesis gives an elementary treatment of this calculus which should be accessible to the non-specialist. The thesis deals also with extensions of the calculus to the composition of a Generalized Function and a Stochastic Variable which makes it applicable to the discontinuous payoffs encountered with Barrier Structures. The thesis makes a mathematical contribution by providing an elementary calculus for the composition of a Generalized function with a Stochastic Variable in the presence of a conditional expectation.