Abstract: In view of the numerical solution of American bond option pricing model, we constructed a fully implicit finite difference scheme and proved the stability of the scheme. Then, the modulusbased matrix splitting iteration methods were applied to solve the linear complementarity problems (LCP), and further compared it with the projected successive overrelaxation (PSOR) iteration method. Numerical experiments verified the effectiveness and robustness of the new methods.

Key words: finite difference scheme; linear complementarity problem； modulusbased matrix splitting iteration method, American bond option model