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The matter of the stability for multi-asset American option pricing problemsis a present remaining challenge. In this paper a general transformation ofvariables allows to remove cross derivative terms reducing the stencil of theproposed numerical scheme and underlying computational cost. Solution of a suchproblem is constructed by starting with a semi-discretization approach followedby a full discretization using exponential time differencing and matrixquadrature rules. To the best of our knowledge the stability of the numericalsolution is treated in this paper for the first time. Analysis of the timevariation of the numerical solution with respect to previous time leveltogether with the use of logarithmic norm of matrices are the basis of thestability result. Sufficient stability conditions on step sizes, that alsoguarantee positivity and boundedness of the solution, are found. Numericalexamples for two and three asset problems justify the stability conditions andprove its competitiveness with other relevant methods.

Computing stable numerical solutions for multidimensional American option pricing problems: a semi-discretization approach