本文提出了基础资产为无红利分配股票的美式看跌期权的第一个闭合计算公式。美式看跌期权赋予其持有人在期权存续期的任一时刻、以约定价格出售股票的权利但非义务。在过去的几十年中，特别是在Black-Scholes模型给出欧式期权的定价公式后，人们在美式期权的定价方面做了大量探索，提出了不少方法，但尚无闭合公式求法。本文提出了一个美式看跌期权提前行权的最优策略，即当且仅当一个美式看跌期权被提前行权时的收益大于其对应的欧式看跌期权的价值时，该美式看跌期权才会被提前行权。基于这一策略，本文提出了一系列紧密关联的定理并最终推出了一个闭合计算公式。另外，基于该闭合公式得出的结论，本文还指出了Merton（1973）有关永久美式看跌期权(perpetual American put option)的模型是不妥的，明确指出永久美式看跌期权（股票无红利）的价格等于该期权的执行价格。This paper proposes a closed form solution for pricing an American put option on a non-dividend paying stock. An American put option grants its holder rights, but not obligation to sell a stock in a fixed price at any time up until maturity. In the past decades, there is no closed form solution for pricing American options although many people made great efforts. In this paper, an optimally early exercise strategy of an American put option on a non-dividend paying stock is set up. That is, an American put option should be early-exercised when the maximum option premium of early exercise is no less than the value of its European counterpart; otherwise, it should not be early-exercised. Based on this strategy, a series of lemmas is proposed and a closed form formula is drawn. Also, this paper shows that Merton (1973)’s formula does not do a good job for pricing perpetual American put options and shows the price of a perpetual American put option on a non-dividend paying stock is equal to the strike price.