  Finite difference approximations to multi-asset American put option price are
considered. The assets are modelled as a multi-dimensional diffusion process
with variable drift and volatility. Approximation error of order one quarter
with respect to the time discretisation parameter and one half with respect to
the space discretisation parameter is proved by reformulating the corresponding
optimal stopping problem as a solution of a degenerate Hamilton-Jacobi-Bellman
equation. Furthermore, the error arising from restricting the discrete problem
to a finite grid by reducing the original problem to a bounded domain is
estimated.
