  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.
