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"]

Cited References (36)

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  2. Evaluating and hedging exotic swap instruments via LGM (2002)
  3. Differential machine learning (2020) — link
  4. The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks (2015) — link
  5. QuantLib
  6. Deep xVA solver: A neural network–based counterparty credit risk management framework (2023) — link
  7. Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models (2021) — link
  8. On a neural network to extract implied information from American options (2021) — link
and 28 more
  1. Variational inequalities and the pricing of American options (1990)
  2. An upwind numerical approach for an A merican and E uropean option pricing model (1998)
  3. QUADRATIC CONVERGENCE FOR VALUING AMERICAN OPTIONS USING A PENALTY METHOD (2002)
  4. Numerical solution of variational inequalities for pricing A sian options by higher order L agrange– G alerkin methods (2006)
  5. Numerical methods for pricing callable bonds with notice (2005)
  6. PDE models for A merican options with counterparty risk and two stochastic factors: Mathematical analysis and numerical solution (2020)
  7. A M onte C arlo approach to A merican options pricing including counterparty risk (2019)
  8. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations (2019) — link
  9. Pricing Bermudan options using regression trees/random forests (2023) — link
  10. Valuing American options by simulation: A simple least-squares approach (2001)
  11. GPU acceleration of the Stochastic Grid Bundling Method for early-exercise options (2015) — link
  12. Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions (2009)
  13. Derivative pricing and risk management with neural networks (2022) — link
  14. A review of neural network applications in derivative pricing, hedging and risk management (2023)
  15. A neural network-based framework for financial model calibration (2019)
  16. Boundary-safe PINNs extension: Application to non-linear parabolic PDEs in counterparty credit risk (2023) — link
  17. Deep joint learning for language recognition (2021) — link
  18. A survey of multi-task learning in natural language processing: Regarding task relatedness and training methods (2022)
  19. Joint learning of localized representations from medical images and reports (2022) — link
  20. Multi-Task Learning with Deep Neural Networks: A Survey (2020) — link
  21. An Overview of Multi-Task Learning in Deep Neural Networks (2017) — link
  22. Rolling Adjoints: Fast Greeks along Monte Carlo scenarios for early-exercise options (2019) — link
  23. A new integral equation formulation for American put options (2018) — link
  24. Efficient parallel Monte-Carlo techniques for pricing American options including counterparty credit risk (2023) — link
  25. Pricing interest-rate-derivative securities (1990)
  26. Modern computational finance: AAD and parallel simulations (2018)
  27. The SABR/LIBOR market model: Pricing, calibration and hedging for complex interest-rate derivatives (2009)
  28. Parsimonious modeling of yield curves (1987) — link

0 of 36 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.