In the framework of uncertainty theory, this paper investigates the pricing problem of American swaption. By assuming that the floating interest rate obeys an uncertain differential equation, the pricing formula of American swaption is derived. Furthermore, parameter estimation of the uncertain interest rate model is given, and the uncertain hypothesis test shows that the uncertain interest rate model fits the Shanghai interbank offered rate well. Finally, as a byproduct, this paper also indicates that stochastic differential equations cannot model real-world interest rates.

中文翻译：

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上海银行间同业拆借利率不确定模型及美式掉期定价

在不确定性理论的框架下，本文研究了美式掉期期权的定价问题。假设浮动利率服从一个不确定的微分方程，推导出美式互换的定价公式。此外，给出了不确定利率模型的参数估计，不确定性假设检验表明，不确定利率模型与上海银行同业拆借利率的拟合较好。最后，作为副产品，本文还指出随机微分方程不能模拟现实世界的利率。