One of the most important issues in American option pricing is to find an optimal exercise strategy, i.e. a time t such that, when the option is exercised at t, the expected discounted payoff of the option is maximised. For some dynamic specifications of the underlying asset price, a characterisation of optimal exercise can be made in terms of an exercise boundary: the optimal strategy consists in exercising the option at the first crossing of the boundary by the underlying asset price. The objective of the project is to derive econometric techniques for estimating the frontier. Several approaches will be considered, depending on which assumptions are made on the underlying dynamics. We will consider parametric estimation where some estimates of the dynamics coefficients are used as the true value in the calculation of the boundary. Non parametric estimation of stochastic frontiers will also be performed. Simulation procedures will be used for assessing thus distributional properties of our estimates. Finally, we will propose a test of the pricing model based on a comparison of different estimators.