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Methods for pricing American options under regime switching. (English) Zbl 1232.91707
Summary: We analyze a number of techniques for pricing American options under a regime switching stochastic process. The techniques analyzed include both explicit and implicit discretizations with the focus being on methods which are unconditionally stable. In the case of implicit methods we also compare a number of iterative procedures for solving the associated nonlinear algebraic equations. Numerical tests indicate that a fixed point policy iteration, coupled with a direct control formulation, is a reliable general purpose method. Finally, we remark that we formulate the American problem as an abstract optimal control problem; hence our results are applicable to more general problems as well.
MSC:
91G60Numerical methods in mathematical finance
91G20Derivative securities
65N06Finite difference methods (BVP of PDE)
93C20Control systems governed by PDE