We propose a deep Recurrent neural network (RNN) framework for computing prices and deltas of American options in high dimensions. Our proposed framework uses two deep RNNs, where one network learns the price and the other learns the delta of the option for each timestep. Our proposed framework yields prices and deltas for the entire spacetime, not only at a given point (e.g. t = 0). The computational cost of the proposed approach is linear in time, which improves on the quadratic time seen for feedforward networks that price American options. The computational memory cost of our method is constant in memory, which is an improvement over the linear memory costs seen in feedforward networks. Our numerical simulations demonstrate these contributions, and show that the proposed deep RNN framework is computationally more efficient than traditional feedforward neural network frameworks in time and memory.
翻译:我们提议了一个用于高维度计算美国选项的价格和三角形的深度经常性神经网络框架(RNN),我们提议的框架使用两个深度RNN,一个网络学习价格,另一个网络学习每个时间步骤的选择的三角形。我们提议的框架不仅在某一点(例如t=0)产生整个空间时间的价格和三角形,而且不仅在某一点(例如t=0)产生。拟议方法的计算成本是线性,这改善了为美国选项定价的向前网络所看到的四轨时间。我们方法的计算内存成本在记忆中是不变的,这比在向前网络所见的线性内存成本有所改进。我们的数字模拟显示了这些贡献,并表明拟议的深度RNNF框架在计算上比在时间和记忆中传统的向上向神经网络框架更有效。