The critical price \(S^{*}\left( t\right) \) of an American put option is the underlying stock price level that triggers its immediate optimal exercise. We provide a new perspective on the determination of the critical price near the option maturity T when the jump-adjusted dividend yield of the underlying stock is either greater than or weakly smaller than the riskfree rate. Firstly, we prove that \(S^{*}\left( t\right) \) coincides with the critical price of the covered American put (a portfolio that is long in the put as well as in the stock). Secondly, we show that the stock price that represents the indifference point between exercising the covered put and waiting until T is the European-put critical price, at which the European put is worth its intrinsic value. Finally, we prove that the indifference point’s behavior at T equals \(S^{*}\left( t\right) \)’s behavior at T when the stock price is either a geometric Brownian motion or a jump-diffusion. Our results provide a thorough economic analysis of \(S^{*}\left( t\right) \) and rigorously show the correspondence of an American option problem to an easier European option problem at maturity .

美式看跌期权的临界价格\(S^{*}\left(t\right) \)是触发其即时最优行使的标的股票价格水平。当标的股票的跳跃调整股息收益率大于或略小于无风险利率时，我们为确定期权到期T附近的临界价格提供了新的视角。首先，我们证明\(S^{*}\left(t\right) \)与有保障的美式看跌期权（在看跌期权和股票中都做多的投资组合）的临界价格一致。其次，我们证明了代表行使受保看跌期权和等待T之间的无差异点的股票价格是欧洲看跌期权的临界价格，在该价格欧洲看跌期权值得其内在价值。最后，我们证明了当股票价格是几何布朗运动或跳跃扩散时，无差异点在T处的行为等于\(S^{*}\left( t\right) \)在T处的行为。我们的结果提供了对\(S^{*}\left(t\right)\)的全面经济分析，并严格显示了美式期权问题与到期日较简单的欧式期权问题的对应关系。