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,广泛用于定价利率衍生品,如欧式和百慕大式掉期权,其中蒙特卡罗模拟已成为行业标准。在低维情况下,使用这些方法可以准确、可靠地定价欧式掉期权,但即使在这个计算上相对简单的情况下,当使用状态变量作为回归器时,它们也会低估百慕大式掉期权的价值。这主要是由于回归中使用的有限数量的预定基函数。此外,在高维度的情况下,这些方法会受到维数灾难的影响。为了解决这些问题,深度学习技术已被用来解决欧式和百慕大式掉期权的价值过程所涉及的反向随机微分方程;然而,这些方法受到训练时间和内存的限制。为了克服这些限制,我们提出利用张量神经网络,因为它们可以提供显著的参数节省,同时达到与经典的密集神经网络相同的精度。在本文中,我们严格评估了张量神经网络和密集神经网络在定价欧式和百慕大式掉期权方面的表现,并且我们表明,相对于密集神经网络,张量神经网络可以更快地训练,同时提供更准确、更可靠的价格。