In this paper, we introduce two methods to solve the American-style option pricing problem and its dual form at the same time using neural networks. Without applying nested Monte Carlo, the first method uses a series of neural networks to simultaneously compute both the lower and upper bounds of the option price, and the second one accomplishes the same goal with one global network. The avoidance of extra simulations and the use of neural networks significantly reduce the computational complexity and allow us to price Bermudan options with frequent exercise opportunities in high dimensions, as illustrated by the provided numerical experiments. As a by-product, these methods also derive a hedging strategy for the option, which can also be used as a control variate for variance reduction.

翻译：本文提出了两种利用神经网络同时求解美式期权定价问题及其对偶形式的方法。第一种方法在不使用嵌套蒙特卡洛模拟的情况下，通过一系列神经网络同时计算期权价格的上下界；第二种方法则通过一个全局网络实现相同目标。由于避免了额外模拟并采用神经网络，计算复杂度显著降低，使得我们能够对具有频繁行权机会的高维百慕大期权进行定价，数值实验验证了这一点。作为副产品，这些方法还推导出期权的对冲策略，该策略也可用作方差缩减的控制变量。