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，广泛应用于欧式与百慕大互换期权的定价，其中蒙特卡洛模拟已成为行业标准。在低维场景下，该方法能为欧式互换期权提供精确且稳健的定价，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，其已知会低估百慕大互换期权的价值。这主要源于回归过程中使用了有限数量的预设基函数。此外，在高维场景下，此类方法会遭遇维度灾难。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，这些方法受限于训练时间和内存。为克服这些局限，我们提出利用张量神经网络，因其能在保持与传统密集神经网络相同精度的同时，实现显著的参数节约。本文严格对比了张量神经网络与密集神经网络在欧式和百慕大互换期权定价中的性能，结果表明张量神经网络的训练速度更快，且其提供的定价比密集神经网络更精准、更稳健。