  The matter of the stability for multi-asset American option pricing problems
is a present remaining challenge. In this paper a general transformation of
variables allows to remove cross derivative terms reducing the stencil of the
proposed numerical scheme and underlying computational cost. Solution of a such
problem is constructed by starting with a semi-discretization approach followed
by a full discretization using exponential time differencing and matrix
quadrature rules. To the best of our knowledge the stability of the numerical
solution is treated in this paper for the first time. Analysis of the time
variation of the numerical solution with respect to previous time level
together with the use of logarithmic norm of matrices are the basis of the
stability result. Sufficient stability conditions on step sizes, that also
guarantee positivity and boundedness of the solution, are found. Numerical
examples for two and three asset problems justify the stability conditions and
prove its competitiveness with other relevant methods.
