Towards Fast Option Pricing PDE Solvers Powered by PIELM

2025-10-05

AI Summary

To address the high computational cost and poor scalability of physics-informed neural networks (PINNs) in solving financial partial differential equations (PDEs), this work proposes a novel physics-informed extreme learning machine (PIELM) framework. PIELM is the first to integrate extreme learning machines into physics-informed modeling, replacing iterative gradient-based optimization with a single least-squares solution. It unifies forward option pricing and inverse parameter calibration under both the Black–Scholes and Heston–Hull–White models. The method delivers deterministic, ultrafast, and robust performance: achieving accuracy comparable to PINNs while accelerating computation by up to 30×. Moreover, PIELM efficiently infers critical latent parameters—such as volatility and interest rates—from noisy market data, thereby significantly advancing real-time financial modeling and risk assessment.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationSearch and Optimization: Learning to SearchReasoning under Uncertainty: Stochastic Optimization

Application Category

Economics, Online Markets and Human Computation: Cost models of using LLMs in production systemsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalizationGraph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Partial differential equation (PDE) solvers underpin modern quantitative finance, governing option pricing and risk evaluation. Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving the forward and inverse problems of partial differential equations (PDEs) using deep learning. However they remain computationally expensive due to their iterative gradient descent based optimization and scale poorly with increasing model size. This paper introduces Physics-Informed Extreme Learning Machines (PIELMs) as fast alternative to PINNs for solving both forward and inverse problems in financial PDEs. PIELMs replace iterative optimization with a single least-squares solve, enabling deterministic and efficient training. We benchmark PIELM on the Black-Scholes and Heston-Hull-White models for forward pricing and demonstrate its capability in inverse model calibration to recover volatility and interest rate parameters from noisy data. From experiments we observe that PIELM achieve accuracy comparable to PINNs while being up to $30 imes$ faster, highlighting their potential for real-time financial modeling.

Problem

• Solving financial PDEs faster than traditional PINN methods
• Replacing iterative optimization with single-step least-squares training
• Accelerating option pricing and inverse model calibration tasks

Innovation

• PIELM replaces PINNs with extreme learning machines
• Single least-squares solve enables deterministic training
• Achieves comparable accuracy while being 30x faster