American Options Pricing under Heston Model via Curriculum Learning in Coupled PINNs

Battle Count: 95

Highly relevant for quantitative finance practitioners dealing with American-style derivatives under stochastic volatility. The mesh-free approach enables fast repeated evaluations after training, suitable for real-time pricing and hedging. Accurate Greeks (Delta, Vega) computation supports risk management. However, the paper focuses on a specific single-asset American put under Heston, limiting immediate applicability to broader trading strategies. The training cost and complexity may limit adoption compared to established numerical methods for production systems.

High complexity due to: (1) coupled two-network architecture with alternating update scheme (10:1 ratio), (2) three-phase curriculum learning with different loss configurations per phase, (3) adaptive resampling requiring periodic regeneration of 150,000 collocation points based on evolving boundary, (4) six separate loss components with phase-dependent weighting, (5) automatic differentiation for second-order PDE derivatives requiring GELU activation, (6) normalization of inputs/outputs, (7) boundary filtering of collocation points. Requires strong understanding of both PINN training and financial PDEs.

Source code is publicly available on GitHub. Detailed hyperparameters (Table 1), network architectures (5 hidden layers with specific neuron counts), activation functions (GELU), optimizer settings (Adam with specific LR and step sizes), collocation point counts (150,000 total), and training phases (1000+3500+2000 epochs) are all specified. Heston model parameters for benchmarking are provided. However, random seeds and exact hardware specifications are not mentioned.