An adaptive-fidelity gradient-enhanced PINN framework for option pricing under regime-switching models

This paper introduces an Adaptive Fidelity Gradient-Enhanced Physics-Informed Neural Network (AF-GPINN) for pricing options under regime-switching models. These models use multiple discrete market states (“regimes”), leading to coupled PDE systems that are computationally challenging. We build upon Physics-Informed Neural Networks (PINNs), which embed PDEs into the loss function. Our method enhances this by incorporating PDE residual gradients (GPINN) for improved accuracy with financial derivatives. The key innovation is a novel adaptive strategy for the total loss function. Training for coupled systems involves balancing many competing terms: PDE residuals and gradients per regime, boundary/initial conditions, and market data. Fixed weights often cause poor performance. Our AF-GPINN framework dynamically adapts these weights during training. Initially, it prioritizes satisfying the physics (PDEs and their gradients) to establish a structurally sound solution. The importance of observational data is then gradually increased. This phased approach refines the solution to match real data without violating physical consistency, generalizing standard PINN/GPINN methods. Numerical experiments on two- and three-regime models validate the framework, demonstrating accurate, efficient option pricing and its potential as a robust tool in financial engineering.