Application of Tensor Neural Networks to Pricing Bermudan Swaptions

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.Comment: 15 pages, 9 figures, 2 table

Procédé d'optimisation d'un processus de calcul dans un processeur binaire classique

[EN] The present invention is related to a method for optimizing a process in a classical binary processor. The invention is a computer implemented method that combines a classical binary processor and a quantum processor wherein the method receives a high-cost instantiated function and instantiates a new function requiring a much lower computational cost. The method, according to a specific embodiment, may be applied iteratively providing a sequence of functions wherein each function requires a lower computational cost in respect to the previous one converging to a very efficient instantiated function.[FR] La présente invention concerne un procédé d'optimisation d'un processus dans un processeur binaire classique. L'invention concerne un procédé mis en œuvre par ordinateur qui combine un processeur binaire classique et un processeur quantique, le procédé recevant une fonction instanciée à coût élevé et instanciant une nouvelle fonction nécessitant de bien moindres coûts de calcul. Le procédé, selon un mode de réalisation spécifique, peut être appliqué de manière itérative à une séquence de fonctions, chaque fonction nécessitant un coût de calcul plus faible par rapport à la précédente convergeant vers une fonction instanciée très efficace.NoBanco Bilbao Vizcaya Argentaria, S.A., Consejo Superior de Investigaciones CientíficasA1 Solicitud de patente con informe sobre el estado de la técnic