We present three models of stock price with time-dependent interest rate, dividend yield, and volatility, respectively, that allow for explicit forms of the optimal exercise boundary of the finite maturity American put option. The optimal exercise boundary satisfies the nonlinear integral equation of Volterra type. We choose time-dependent parameters of the model so that the integral equation for the exercise boundary can be solved in the closed form. We also define the contracts of put type with time-dependent strike price that support the explicit optimal exercise boundary.

中文翻译：

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美式看跌期权的封闭式最优行权边界

我们分别提出了三种具有时间相关利率、股息收益率和波动率的股票价格模型，它们允许有限期限美式看跌期权的最佳行使边界的明确形式。最优运动边界满足Volterra型非线性积分方程。我们选择模型的时间相关参数，以便可以以封闭形式求解运动边界的积分方程。我们还定义了具有时间相关执行价格的看跌期权合约，支持明确的最佳行使边界。