Abstract
We present a method to solve the free-boundary problem that arises in the pricing of classical American options. Such free-boundary problems arise when one attempts to solve optimal-stopping problems set in continuous time. American option pricing is one of the most popular optimal-stopping problems considered in literature. The method presented in this paper primarily shows how one can leverage on a one factor approximation and the moving boundary approach to construct a solution mechanism. The result is an algorithm that has superior runtimes-accuracy balance to other computational methods that are available to solve the free-boundary problems. Exhaustive comparisons to other pricing methods are provided. We also discuss a variant of the proposed algorithm that allows for the computation of only one option price rather than the entire price function, when the requirement is such.
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