Physics-Informed Neural Networks for Option Pricing and Hedging in Illiquid Jump Markets

Manglam Kartik, Neel Tushar Shah

Abstract: We present a novel Physics-Informed Neural Network (PINN) framework for option pricing and hedging under a Merton-type jump-diffusion model with liquidity costs. Our approach encodes a jump-diffusion pricing partial integro-differential equation (PIDE) with an additional liquidity adjustment in the hedging loss. We establish theoretical guarantees by extending recent PINN convergence results to our setting, and we discuss the well-posedness of the liquidity-adjusted PIDE. We perform extensive experiments on synthetic jump-diffusion data and on real options (e.g. NIFTY50) with sparse observations. An ablation study examines variants removing the jump component, omitting the hedging-loss term, and comparing PDE-constrained vs. data-only training. We also test robustness to jump intensity and liquidity penalty. Our full PINN yields significantly lower pricing RMSE and hedging costs than baselines, including a PINN using only the standard Black–Scholes PDE, and a neural-SDE model. We provide detailed model and training specifications (network architecture, activations, optimizer and schedule, collocation/data points). Visualizations illustrate the learned price surface V (S, t), the learned local volatility surface σ(S, t), hedging P&L distributions, and any arbitrage-constraint violations. Finally, we discuss broader impacts: potential benefits for brokers and fintech firms, and risks of model misuse or systemic “model monoculture” in AI-driven trading. Our paper is organized as follows.