A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options
A deep learning approach for computations of exposure profiles for high-dimensional Bermudan options
复制标题
用于计算高维百慕大期权暴露剖面的深度学习方法
DOI：
10.1016/j.amc.2021.126332
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
C. Oosterlee
中科院分区：
文献类型：
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作者：
Kristoffer Andersson;C. Oosterlee
在本文中，我们提出了一个基于神经网络的方法来近似的预期风险和潜在的未来风险的黄金期权。在第一阶段，该方法依赖于Becker，Cheridito和Jentzen（2019）提出的深度最优停止算法（DOS），该算法从潜在风险因素的蒙特-卡罗样本中学习最优停止规则。现金流路径，然后通过应用学习停止策略的一组新的实现的风险因素。此外，在第二阶段的现金流路径预测到风险因素，以获得近似的路径选项的价值。回归步骤进行普通最小二乘法以及神经网络，它表明，后者的结果更准确的近似。制定的预期风险，无论是在现金流路径和路径选项的价值，它表明，一个简单的蒙特-卡罗平均产量在这两种情况下准确的近似。潜在的未来暴露是通过经验α百分位数来估计的。最后，它表明，预期的风险，以及潜在的未来风险可以计算下，风险中性的措施，或真实的世界的措施，而不必重新训练的神经网络。
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 (DOS) proposed by Becker, Cheridito, and Jentzen (2019), 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 cashflow paths are projected onto the risk factors 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 results in 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.