American put options are among the most frequently traded single stock options, and their calibration is computationally challenging since no closed-form expression is available. Due to their higher flexibility compared with European options, the mathematical model involves additional constraints, and a variational inequality is obtained. We use the Heston stochastic volatility model to describe the price of a single stock option. In order to speed up the calibration process, we apply two model-reduction strategies. First, we introduce a reduced basis method. We thereby reduce the computational complexity of solving the parametric partial differential equation drastically, compared with a classical finite-element method, which makes applications of standard minimization algorithms for the calibration significantly faster. Second, we apply the so-called de-Americanization strategy. Here, the main idea is to reformulate the calibration problem for American options as a problem for European options and to exploit closed-form solutions. These reduction techniques are systematically compared and tested for both synthetic and market data sets.

中文翻译：

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降低校准美式期权的复杂性

美式看跌期权是交易最频繁的单一股票期权之一，它们的校准在计算上具有挑战性，因为没有封闭形式的表达式可用。由于与欧式期权相比具有更高的灵活性，数学模型涉及额外的约束，并获得了变分不等式。我们使用 Heston 随机波动率模型来描述单个股票期权的价格。为了加快校准过程，我们应用了两种模型缩减策略。首先，我们介绍一种约简基方法。因此，与经典的有限元方法相比，我们大大降低了求解参数偏微分方程的计算复杂度，这使得标准最小化算法的校准应用速度显着加快。第二，我们采用所谓的去美国化战略。在这里，主要思想是将美式期权的校准问题重新表述为欧式期权的问题，并利用封闭形式的解决方案。这些减少技术针对合成数据集和市场数据集进行了系统比较和测试。