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.

本文介绍使用 Tensor Neural Networks 模型来有效解决利率衍生品 Cheyette 模型中 Bermudan Swaption 价格低估的问题，并证明该模型能够提供比传统密集神经网络（Dense Neural Networks）更快的训练速度和更准确的价格估计。

基于张量神经网络的百慕大掉期定价应用

Application of Tensor Neural Networks to Pricing Bermudan Swaptions

Partial Differential Equations (PDEs) are used to model a variety of
dynamical systems in science and engineering. Recent advances in deep learning
have enabled us to solve them in a higher dimension by addressing the curse of
dimensionality in new ways. However, deep learning methods are constrained by
training time and memory. To tackle these shortcomings, we implement Tensor
Neural Networks (TNN), a quantum-inspired neural network architecture that
leverages Tensor Network ideas to improve upon deep learning approaches. We
demonstrate that TNN provide significant parameter savings while attaining the
same accuracy as compared to the classical Dense Neural Network (DNN). In
addition, we also show how TNN can be trained faster than DNN for the same
accuracy. We benchmark TNN by applying them to solve parabolic PDEs,
specifically the Black-Scholes-Barenblatt equation, widely used in financial
pricing theory, empirically showing the advantages of TNN over DNN. Further
examples, such as the Hamilton-Jacobi-Bellman equation, are also discussed.

本文介绍了如何通过 Tensor Neural Networks 来解决 Partial Differential Equations 的问题，实现了与 Deep Neural Network 同样精度的情况下更小的参数及更快的训练速度，并以 Black-Scholes-Barenblatt equation 模型为例进行了测试验证。