A ‘moving index’ method for the solution of the American options valuation problem

We introduce a new technique for the solution of the American options valuation problem, which resembles the moving boundary behavior of the solution, and thus, we call it the ‘moving index’ (MI) method. We use the so-called linear complementarity formulation of the problem for which projected successive over relaxation (PSOR) is a leading and well-known method. We report on experimental results, which demonstrate that our MI method presents dramatic improvements over PSOR since it is several times faster for a given desired accuracy. There are also cases in which the MI method continues to perform well, while it is impossible to achieve the desired accuracy with PSOR within a decent time interval.