Abstract: We proposed an efficient algorithm for the pricing problem of American multi-asset option. Firstly, by using the penalty method and the perfectly matched layer technique, we transformed the linear complementary model satisfied by multi-asset option into a nonlinear parabolic problem on a bounded domain. Secondly, a semi-implicit finite difference method was used to solve the transformed nonlinear problem, and we gave the error results of the method and the nonnegative proof of the numerical solution. Finally, numerical experiments were used to verify the practicability and effectiveness of the proposed algorithm.

Key words: American multi-asset option, semi-implicit finite difference method, perfectly matched layer (PML)