American Option Pricing Using Malliavin Calculus

The Malliavin calculus is an especially promising tool for solving the pricing problem of American options under a constant volatility, and also when the volatility is stochastic. Using the Malliavin calculus, the aim of this work consisted computing the conditional expectation, related to the solution of the pricing problem of the American option, for the uni and bi-dimensional model, as a suitable ratio of ordinal expectations. The estimation of this ratio became possible by using the Monte Carlo simulations.