A Comparison of Iterated Optimal Stopping and Local Policy Iteration for American Options Under Regime Switching

A theoretical analysis tool, iterated optimal stopping, has been used as the basis of a numerical algorithm for American options under regime switching [19]. Similar methods have also been proposed for American options under jump diffusion [3] and Asian options under jump diffusion [4]. We show that a re-arrangement of the numerical algorithm in the form of local policy iteration [21, 17] has provabably superior bounds on the convergence rate, and requires less storage. Numerical tests are presented which are consistent with the theoretical bounds.