Paper: arXiv 2410.10474

Abstract

In this article, we employ physics-informed residual learning (PIRL) and propose a pricing method for European options under a regime-switching framework, where closed-form solutions are not available. We demonstrate that the proposed approach serves an efficient alternative to competing pricing techniques for regime-switching models in the literature. Specifically, we demonstrate that PIRLs eliminate the need for retraining and become nearly instantaneous once trained, thus, offering an efficient and flexible tool for pricing options across a broad range of specifications and parameters.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces advanced mathematics through regime-switching models and physics-informed neural networks (PIRL), with heavy derivations and PDE formulations. However, it lacks empirical data, backtests, or code, focusing instead on theoretical methodology and numerical experiments within a controlled academic setting.

Research Flowchart

  flowchart TD
  A["Research Goal: European Option Pricing in Regime-Switching Models"] --> B["Key Methodology: Physics-Informed Residual Learning PIRL"]
  B --> C["Data Inputs: Market Data & Regime Probabilities"]
  B --> D["Computational Process: Train PIRL to satisfy Black-Scholes PDE"]
  C --> D
  D --> E["Outcome 1: No closed-form solution required"]
  D --> F["Outcome 2: Near-instantaneous pricing post-training"]
  D --> G["Outcome 3: Flexible across parameters & regimes"]

Cited References (39)

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  6. An analytical approximation formula for E uropean option pricing under a new stochastic volatility model with regime-switching (2016)
  7. A new exact solution for pricing E uropean options in a two-state regime-switching economy (2012)
  8. Regime switching and E uropean options (2002)
and 31 more
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  2. Deep residual learning for image recognition (2016)
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  5. A neural network approach for credit risk evaluation (2008) — link
  6. Natural language processing (2020)
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  10. Machine learning for pricing A merican options in high-dimensional M arkovian and non- M arkovian models (2020) — link
  11. Predicting the stock price of frontier markets using machine learning and modified B lack– S choles Option pricing model (2020) — link
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  13. hp- VPINNs : V ariational physics-informed neural networks with domain decomposition (2021)
  14. B-PINNs : B ayesian physics-informed neural networks for forward and inverse PDE problems with noisy data (2021)
  15. Piat: P hysics informed adversarial training for solving partial differential equations (2022) — link
  16. On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models (2023) — link
  17. Physics Informed Deep Learning for Traffic State Estimation (2020) — link
  18. Physics-Informed Deep Learning for Traffic State Estimation: A Hybrid Paradigm Informed By Second-Order Traffic Models (2021)
  19. A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation (2022) — link
  20. Empirical Asset Pricing via Ensemble G aussian Process Regression — → 2212.01048
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  22. Machine learning for quantitative finance: fast derivative pricing, hedging and fitting (2018)
  23. Empirical deep hedging (2023)
  24. Physics-Informed Deep Learning for Traffic State Estimation: Illustrations With LWR and CTM Models (2022) — link
  25. Option pricing in the H eston model with physics inspired neural networks (2024)
  26. Valuation of guaranteed minimum accumulation benefits ( GMAB s) with physics-inspired neural networks (2023)
  27. Option Pricing and Local Volatility Surface by Physics-Informed Neural Network (2024)
  28. A deep learning based numerical PDE method for option pricing (2023)
  29. Why R es N et Works? Residuals Generalize (2020) — link
  30. Power-enhanced residual network for function approximation and physics-informed inverse problems (2024) — link
  31. A physics-informed data-driven algorithm for ensemble forecast of complex turbulent systems (2024) — link

1 of 39 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.