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.