The Cheyette model is a quasi-Gaussian volatility interest rate model widely used to price interest rate derivatives such as European and Bermudan Swaptions for which Monte Carlo simulation has become the industry standard. In low dimensions, these approaches provide accurate and robust prices for European Swaptions but, even in this computationally simple setting, they are known to underestimate the value of Bermudan Swaptions when using the state variables as regressors. This is mainly due to the use of a finite number of predetermined basis functions in the regression. Moreover, in high-dimensional settings, these approaches succumb to the Curse of Dimensionality. To address these issues, Deep-learning techniques have been used to solve the backward Stochastic Differential Equation associated with the value process for European and Bermudan Swaptions; however, these methods are constrained by training time and memory. To overcome these limitations, we propose leveraging Tensor Neural Networks as they can provide significant parameter savings while attaining the same accuracy as classical Dense Neural Networks. In this paper we rigorously benchmark the performance of Tensor Neural Networks and Dense Neural Networks for pricing European and Bermudan Swaptions, and we show that Tensor Neural Networks can be trained faster than Dense Neural Networks and provide more accurate and robust prices than their Dense counterparts.

翻译：Cheyette模型是一种准高斯波动率利率模型，广泛应用于欧洲式和百慕大式互换期权等利率衍生品定价，其中蒙特卡洛模拟已成为行业标准。在低维情形下，这些方法能为欧式互换期权提供准确且稳健的定价结果，但即便在这种计算简单的设定中，当使用状态变量作为回归变量时，已知这些方法会低估百慕大式互换期权的价值。这主要源于回归过程中使用了有限个预设基函数。此外，在高维设定中，这些方法会遭遇维数灾难。为解决这些问题，深度学习技术已被用于求解与欧式和百慕大式互换期权价值过程相关的倒向随机微分方程；然而，这些方法受到训练时间和内存的限制。为克服这些局限，我们提出利用张量神经网络，因为该网络能在保持与经典稠密神经网络相同精度的同时，显著节省参数量。本文严格对比了张量神经网络与稠密神经网络在欧式和百慕大式互换期权定价中的性能，并证明张量神经网络可比稠密神经网络训练更快，且能提供比稠密网络更准确、更稳健的定价结果。