SIAM Journal on Financial Mathematics, Volume 11, Issue 1, Page 201-239, January 2020.
We develop a mixed least squares Monte Carlo--partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets under stochastic volatility. The algorithm is formulated for an arbitrary number of assets and volatility processes, and we prove the algorithm converges almost surely for a class of models. We also introduce a multilevel Monte Carlo/multigrid method to improve the algorithm's computational complexity. Our numerical examples focus on the single ($2d$) and multidimensional (4d) Heston models, and we compare our hybrid algorithm with classical LSMC approaches. In each case, we find that the hybrid algorithm outperforms standard LSMC in terms of estimating prices and optimal exercise boundaries.

中文翻译：

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混合使用LSMC和PDE方法定价百慕大期权

SIAM金融数学期刊，第11卷，第1期，第201-239页，2020年1月。
我们开发了一种混合最小二乘蒙特卡洛-偏微分方程（LSMC-PDE）方法，用于对随机波动性下的百慕大群岛期权定价。该算法是针对任意数量的资产和波动过程制定的，我们证明了该算法对于一类模型几乎可以收敛。我们还引入了多级蒙特卡洛/多重网格方法来提高算法的计算复杂度。我们的数值示例着重于单一（$ 2d $）和多维（4d）Heston模型，我们将混合算法与经典LSMC方法进行了比较。在每种情况下，我们发现在估计价格和最佳行使范围方面，混合算法均优于标准LSMC。