论文标题
一种深度学习方法，用于计算高维百慕大选项的曝光概况
A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options
论文作者
论文摘要
在本文中，我们提出了一种基于神经网络的方法，用于近似预期的暴露和潜在的百慕大期权暴露。在第一阶段，该方法依赖于最佳的最佳停止算法，该算法从蒙特卡洛样本中学习了最佳的停止规则。然后，通过将学习的停止策略应用于对风险因素的一系列新的实现来创建现金流量。此外，在第二阶段，风险因素会根据现金流量路径进行回归，以获得路径方案值的近似值。回归步骤由普通的最小二乘和神经网络进行，并显示后者产生更准确的近似值。 无论是根据现金流量路径还是在路径方向值值方面，都会提出预期的暴露，并表明在这两种情况下，简单的蒙特卡罗平均平均值均可准确地近似。潜在的未来暴露是通过经验$α$ /百分比估计的。 最后，可以证明，预期的暴露以及潜在的未来暴露可以在风险中性度量或现实世界中计算，而无需重新培训神经网络。
In this paper, we propose a neural network-based method for approximating expected exposures and potential future exposures of Bermudan options. In a first phase, the method relies on the Deep Optimal Stopping algorithm, which learns the optimal stopping rule from Monte-Carlo samples of the underlying risk factors. Cashflow-paths are then created by applying the learned stopping strategy on a new set of realizations of the risk factors. Furthermore, in a second phase the risk factors are regressed against the cashflow-paths to obtain approximations of pathwise option values. The regression step is carried out by ordinary least squares as well as neural networks, and it is shown that the latter produces more accurate approximations. The expected exposure is formulated, both in terms of the cashflow-paths and in terms of the pathwise option values and it is shown that a simple Monte-Carlo average yields accurate approximations in both cases. The potential future exposure is estimated by the empirical $α$-percentile. Finally, it is shown that the expected exposures, as well as the potential future exposures can be computed under either, the risk neutral measure, or the real world measure, without having to re-train the neural networks.
