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"]