Projection And Contraction Method For Pricing American Put Options Under Regime-switching

This paper mainly focuses on pricing American put options under regime-switching,which can be described as a problem of variational inequality on a two-dimensional unbounded domain.First,the original pricing model is transformed into a linear complementarity problem on a bounded domain by the prior estimations of the option prices and optimal exercise boundaries,and far-field truncation techniques.After the above processing,the simplified model can be discretized by using the classical difference method.The existence and uniqueness of the solution,as well as the stability and convergence of the difference system,can be readily verified.Furthermore,in view of the positive definiteness of the discrete system matrix,we use the projection and contraction method to obtain the option prices,moreover,give the convergence analysis of the algorithm.Finally,numerical experiments are conducted to demonstrate the correctness and feasibility of the projection and contraction method.