中文摘要：

考虑Black-Scholes模型下美式看跌期权的定价问题。采用有限差分法和 Newton法耦合求解Black-Scholes方程，得到了期权价格和最佳实施边界的数值逼近结果。数值实验验证了算法的有效性。

英文摘要：

This paper deals with the American put option pricing problem governed by the Black-Scholes equation.Applying finite difference method coupled with Newton’s method to solve the Black-Scholes equation,we can get the numerical approximations of the option price and the optimal exercise boundary simultaneously.Numerical experiments verify the efficiency of the method.