英文标题：
《Pricing American Options by Exercise Rate Optimization》
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作者：
Christian Bayer, Ra\\\'ul Tempone, S\\\"oren Wolfers
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最新提交年份：
2019
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英文摘要：
We present a novel method for the numerical pricing of American options based on Monte Carlo simulation and the optimization of exercise strategies. Previous solutions to this problem either explicitly or implicitly determine so-called optimal exercise regions, which consist of points in time and space at which a given option is exercised. In contrast, our method determines the exercise rates of randomized exercise strategies. We show that the supremum of the corresponding stochastic optimization problem provides the correct option price. By integrating analytically over the random exercise decision, we obtain an objective function that is differentiable with respect to perturbations of the exercise rate even for finitely many sample paths. The global optimum of this function can be approached gradually when starting from a constant exercise rate. Numerical experiments on vanilla put options in the multivariate Black-Scholes model and a preliminary theoretical analysis underline the efficiency of our method, both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of the exercise rates. Finally, we demonstrate the flexibility of our method through numerical experiments on max call options in the classical Black-Scholes model, and vanilla put options in both the Heston model and the non-Markovian rough Bergomi model.
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中文摘要：
我们提出了一种基于蒙特卡罗模拟和行权策略优化的美式期权数值定价新方法。该问题的先前解决方案可以显式或隐式地确定所谓的最佳行使区域，该区域由行使给定期权的时间点和空间点组成。相反，我们的方法决定了随机运动策略的运动率。我们证明了相应随机优化问题的上确界提供了正确的期权价格。通过对随机运动决策进行解析积分，我们得到了一个目标函数，即使对于有限多个样本路径，该函数对于运动速率的扰动也是可微的。从恒定运动速率开始，该函数的全局最优值可以逐渐逼近。在多元Black-Scholes模型中对香草看跌期权进行的数值实验和初步的理论分析表明，我们的方法在时间离散化步骤数量和运动率参数化所需的自由度数量方面都是有效的。最后，我们通过经典Black-Scholes模型中的最大看涨期权和Heston模型和非马尔可夫粗糙Bergomi模型中的香草看跌期权的数值实验，证明了我们方法的灵活性。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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