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Finite difference approximations to multi-asset American put option price areconsidered. The assets are modelled as a multi-dimensional diffusion processwith variable drift and volatility. Approximation error of order one quarterwith respect to the time discretisation parameter and one half with respect tothe space discretisation parameter is proved by reformulating the correspondingoptimal stopping problem as a solution of a degenerate Hamilton-Jacobi-Bellmanequation. Furthermore, the error arising from restricting the discrete problemto a finite grid by reducing the original problem to a bounded domain isestimated.

Error estimates for finite difference approximations of American put option price