Paper: arXiv 2404.11257

Abstract

This paper addresses the problem of pricing involved financial derivatives by means of advanced of deep learning techniques. More precisely, we smartly combine several sophisticated neural network-based concepts like differential machine learning, Monte Carlo simulation-like training samples and joint learning to come up with an efficient numerical solution. The application of the latter development represents a novelty in the context of computational finance. We also propose a novel design of interdependent neural networks to price early-exercise products, in this case, Bermudan swaptions. The improvements in efficiency and accuracy provided by the here proposed approach is widely illustrated throughout a range of numerical experiments. Moreover, this novel methodology can be extended to the pricing of other financial derivatives.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced deep learning concepts (Differential Machine Learning, joint/interdependent networks) and sophisticated mathematical formulations for PDEs and free-boundary problems, while providing extensive numerical experiments and efficiency/accuracy comparisons that demonstrate backtest-ready methodology for pricing Bermudan swaptions.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Efficient Pricing of Bermudan Swaptions"] --> B["Methodology: Deep Joint Learning"]
  B --> C["Inputs: Monte Carlo Simulated Data<br>+ Differential ML Features"]
  C --> D["Computational Process<br>Interdependent Neural Networks"]
  D --> E{"Key Findings"}
  E --> F["High Efficiency & Accuracy"]
  E --> G["Proven via Numerical Experiments"]
  E --> H["Generalizable to Other Derivatives"]