An Efficient Machine Learning Framework for Option Pricing via Fourier Transform

2025-12-17

AI Summary

In dynamic markets, option pricing models require frequent recalibration, yet conventional Fast Fourier Transform (FFT) methods suffer from numerical instability—particularly for deep out-of-the-money options and inconsistent input specifications. To address this, we propose a surrogate pricing framework integrating the Smooth Offset Algorithm (SOA) with supervised learning. For the first time, high-fidelity training data generated by SOA is leveraged to train neural networks, random forests, and gradient-boosted trees, yielding a path-independent real-time valuation operator for exponential Lévy processes. Our approach overcomes intrinsic limitations of FFT: the surrogate models accelerate computation by over an order of magnitude relative to SOA alone, while significantly improving accuracy and robustness for out-of-the-money options. The framework supports parallel, high-precision, real-time valuation across multiple contracts.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Other Foundations of Machine Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The increasing need for rapid recalibration of option pricing models in dynamic markets places stringent computational demands on data generation and valuation algorithms. In this work, we propose a hybrid algorithmic framework that integrates the smooth offset algorithm (SOA) with supervised machine learning models for the fast pricing of multiple path-independent options under exponential Lévy dynamics. Building upon the SOA-generated dataset, we train neural networks, random forests, and gradient boosted decision trees to construct surrogate pricing operators. Extensive numerical experiments demonstrate that, once trained, these surrogates achieve order-of-magnitude acceleration over direct SOA evaluation. Importantly, the proposed framework overcomes key numerical limitations inherent to fast Fourier transform-based methods, including the consistency of input data and the instability in deep out-of-the-money option pricing.

Problem

• Accelerates option pricing under exponential Lévy dynamics
• Overcomes limitations of fast Fourier transform methods
• Enables rapid recalibration in dynamic markets

Innovation

• Hybrid framework integrates smooth offset algorithm with machine learning
• Trains neural networks, random forests, and gradient boosted decision trees
• Overcomes fast Fourier transform limitations in data consistency and stability