An American option is a derivative security that can be exercised at any time before expiration.Under standard hypotheses it can be shown that its arbitrage-free price is the solution of an optimal stopping problem.Usually, if Ornament the underlying asset follows a diffusion, the stopping time problem does not have a closed form solution.Therefore, Scoop Plus discrete time models have been proposed to determine an approximated solution.
I formulate some conditions on the discrete process to insure convergence of the approximations to the exact value.I also show how to apply such conditions to check the correctness of some of the most popular discretization schemes.