Paper: arXiv 2304.09750

Authors: Raj G. Patel, Tomas Dominguez, Mohammad Dib, Samuel Palmer, Andrea Cadarso, Fernando De Lope Contreras, Abdelkader Ratnani, Francisco Gomez Casanova, Senaida Hernández-Santana, Álvaro Díaz-Fernández, Eva Andrés, Jorge Luis-Hita, Escolástico Sánchez-Martínez, Samuel Mugel, Roman Orus

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces Tensor Neural Networks to solve BSDEs for high-dimensional pricing in Cheyette interest rate models, effectively tackling the Curse of Dimensionality. It provides a solid theoretical foundation and rigorous benchmarking against standard Dense Neural Networks, demonstrating improved training speed and accuracy.

Research Flowchart

  flowchart TD
    A[Research Goal: Efficiently Price Bermudan Swaptions & Overcome Curse of Dimensionality] --> B[Inputs: Cheyette Model Dynamics & Backward SDE Formulation]
    B --> C[Methodology: Benchmark Tensor Neural Networks vs Dense Neural Networks]
    C --> D[Computational Process: Train Networks on Monte Carlo Simulated State Variable Paths]
    D --> E[Outcome: TNNs Reduce Parameters & Training Time vs DNNs]
    D --> F[Outcome: TNNs Achieve Higher Accuracy & Robustness in High Dimensions]