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We present a multigrid iterative algorithm for solving a system of coupledfree boundary problems for pricing American put options with regime-switching.The algorithm is based on our recently developed compact finite differencescheme coupled with Hermite interpolation for solving the coupled partialdifferential equations consisting of the asset option and the delta, gamma, andspeed sensitivities. In the algorithm, we first use the Gauss-Seidel method asa smoother and then implement a multigrid strategy based on modified cycle(M-cycle) for solving our discretized equations. Hermite interpolation withNewton interpolatory divided difference (as the basis) is used in estimatingthe coupled asset, delta, gamma, and speed options in the set of equations. Anumerical experiment is performed with the two- and four- regime examples andcompared with other existing methods to validate the optimal strategy. Resultsshow that this algorithm provides a fast and efficient tool for pricingAmerican put options with regime-switching.

Multigrid Iterative Algorithm based on Compact Finite Difference Schemes and Hermite interpolation for Solving Regime Switching American Options