中文摘要：

1 引言 期权是最重要的金融衍生工具之一，是一种客观的选择权，它赋予其购买者一种在规定期限内按交易双方约定的价格（敲定价）购买或出售一定数量的某种金融资产的权利．利用期权人们可以有效的回避风险，每天在交易所都有大量的交易．

英文摘要：

In this paper, based on the modification of Crank-Nicolson scheme, we present a new numerical method for the problem of the price of American put option. By using the energy methods, we analyze the stability, convergence and error estimation of this method. Numerical results show that the method is effective.