考虑有限元方法结合模方法定价美式期权.基于线性有限元空间,构造了Black-Scholes方程的向后欧拉和Crank-Nicolson两种全离散有限元格式.采用模超松弛迭代方法求解有限元离散得到的线性互补问题,并建立H+-离散矩阵下模超松弛迭代(MSOR)方法的收敛定理.数值实验验证了本文方法的有效性,也说明MSOR方法的计算效率优于投影超松弛迭代(PSOR)方法.%In this paper,a modulus method based on finite element discretization is introduced to price American option.Based on a linear finite element space,backward Euler and Crank-Nicolson finite element schemes of the Black-Scholes equation are constructed.The modulus-based successive overrelaxation(MSOR) method are applied to solve the resulted linear complementarity problems(LCPs).Further, the H+-matrix property of the discretization matrix which guarantees the convergence of the MSOR method is also analyzed.Numerical experiments show the efficient of the proposed method,and illustrate that the MSOR method outperforms the projected successive overrelaxation method(PSOR).
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