We investigate two new strategies for the numerical solution of optimal stopping problems within the Regression Monte Carlo (RMC) framework of Longstaff and Schwartz. First, we propose the use of stochastic kriging (Gaussian process) meta-models for fitting the continuation value. Kriging offers a flexible, nonparametric regression approach that quantifies approximation quality. Second, we connect the choice of stochastic grids used in RMC to the Design of Experiments paradigm. We examine space-filling and adaptive experimental designs; we also investigate the use of batching with replicated simulations at design sites to improve the signal-to-noise ratio. Numerical case studies for valuing Bermudan Puts and Max-Calls under a variety of asset dynamics illustrate that our methods offer significant reduction in simulation budgets over existing approaches.

中文翻译：

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百慕大期权定价的克里金元模型和实验设计

我们研究了 Longstaff 和 Schwartz 的回归蒙特卡罗 (RMC) 框架内最优停止问题的数值解的两种新策略。首先，我们建议使用随机克里金法（高斯过程）元模型来拟合连续值。克里金法提供了一种灵活的非参数回归方法，可以量化近似质量。其次，我们将 RMC 中使用的随机网格的选择与实验设计范式联系起来。我们研究了空间填充和适应性实验设计；我们还研究了在设计站点使用批处理和复制模拟来提高信噪比。