### Abstract:

In this study,we consider two problems.The first one is the problem of computing hedging
portfolios for options that may have discontinuous payoff functions.For this problem we use the Malliavin property called the Clark-Ocone formula and give some examples for diferent types of pay of functions of the options of European type.The second problem is based on the
computation of price sensitivities (derivatives of the probabilistic representation of the pay off
functions with respect to the underlying parameters of the model) also known as`Greeks'
of discontinuous payoff functions and also give some examples.We restrict ourselves to the
computation of Delta, Gamma and Vega.For this problem we make use of the properties
of the Malliavin calculus like the integration by parts formula and the chain rule.We find
the representations of the price sensitivities in terms of the expected value of the random
variables that do not involve the actual direct differentiation of the payout function,that is,
E[g(XT ) ] where g is a payoff function which depend on the stochasticdic differential equation
XT at maturity time T and is the Malliavin weigh tfunction. In general, we study the
regularity of the solutions of the stochastic differentia lequations in the sense of Malliavin
calculus and explore its applications to Mathematical finance.