Adaptive PINO Heston Option Pricing Engine (Simplified)
🎯 Project Summary
This project develops a state-of-the-art solution for pricing European options under the Heston Stochastic Volatility Model. We utilize a hybrid Physics-Informed Neural Operator (PINO), combining the high-speed processing of the Fourier Neural Operator (FNO) with the stability of Adaptive Learning (WamOL).
Core Goal: To create an instantaneous and accurate pricing model that can replace slow and unstable numerical methods (Monte Carlo and FFT) for real-time financial calibration.
The Problem
Traditional Heston pricing methods are computationally expensive. Monte Carlo is too slow, and Fast Fourier Transform (FFT) suffers from numerical instability and requires manual tuning for different volatility regimes.
Our Solution
We train the neural network to solve the Feynman-Kac PDE (the governing physics equation) across the entire parameter space. Advanced techniques used include:
FNO Backbone: Ensures efficient learning and high-speed prediction.
Hard Ansatz Transform: Guarantees structural stability by satisfying the terminal payoff boundary condition analytically.
WamOL Adaptive Loss: Automatically balances multiple physics constraints (PDE, Delta, Gamma smoothness) during training, optimizing for uniform accuracy.
📈 Current Results & Next Steps
Our initial tests confirm the framework's operational efficiency but highlight a capacity issue:
Metric
Finding
Status
Computational Speed
273.8X Speedup over Monte Carlo
CONFIRMED VIABLE
Accuracy (MAE)
$2.75 Mean Absolute Error
INSUFFICIENT
Next Step: The current model is limited by VRAM, preventing training on a necessary high-resolution grid (targeting