The constant elasticity of variance (CEV) model is a practical approach to option pricing by fitting to the implied volatility smile. However, pricing American options is computationally intensive because no analytical formulas are available. In this paper, we present numerical methods to find the optimal exercise boundary with respect to an American put option under the CEV model. This problem corresponds to the free boundary (also called an optimal exercise boundary) problem for a partial differential equation. We use a transformed function that has Lipschitz character near the optimal exercise boundary to determine the optimal exercise boundary. After determining the optimal exercise boundary, we calculate American put option values under the CEV model using the finite-difference method. Finally, we use the proposed numerical method to obtain several results that are then compared with the results of other methods.

恒定弹性方差（CEV）模型是一种适合隐含波动率微笑的期权定价实用方法。但是，由于没有可用的分析公式，因此对美式期权进行定价需要大量计算。在本文中，我们提出了在CEV模型下针对美国认沽期权找到最佳行使边界的数值方法。该问题对应于偏微分方程的自由边界（也称为最佳运动边界）问题。我们使用在最佳运动边界附近具有Lipschitz特征的变换函数来确定最佳运动边界。在确定最佳行使边界之后，我们使用有限差分法在CEV模型下计算美式看跌期权价值。最后，