Enhancing Fourier pricing with machine learning

Paper: arXiv 2412.05070

Authors: Gero Junike, Hauke Stier

Abstract

Fourier pricing methods such as the Carr-Madan formula or the COS method are classic tools for pricing European options for advanced models such as the Heston model. These methods require tuning parameters such as a damping factor, a truncation range, a number of terms, etc. Estimating these tuning parameters is difficult or computationally expensive. Recently, machine learning techniques have been proposed for fast pricing: they are able to learn the functional relationship between the parameters of the Heston model and the option price. However, machine learning techniques suffer from error control and require retraining for different error tolerances. In this research, we propose to learn the tuning parameters of the Fourier methods (instead of the prices) using machine learning techniques. As a result, we obtain very fast algorithms with full error control: Our approach works with any error tolerance without retraining, as demonstrated in numerical experiments using the Heston model.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel paradigm shift in ML-assisted option pricing: instead of directly predicting prices (which lacks error control), it uses machine learning to predict hyper-parameters of traditional Fourier pricing methods. The mathematical formulation is sound, leveraging moment derivatives and Fourier analysis under the Heston model, and is supported by clear numerical experiments.

Research Flowchart

  flowchart TD
    A["<b>Research Goal</b><br/>Achieve fast option pricing with strict error control using ML"] --> B["<b>Inputs & Models</b><br/>Heston Model Parameters & Target Error Tolerances"]
    
    subgraph Methodology["Proposed Methodology"]
        B --> C["<b>ML Parameter Tuning</b><br/>Train ML model to predict Fourier/COS tuning parameters"]
        C --> D["<b>Fourier Pricing Execution</b><br/>Apply predicted parameters to Carr-Madan / COS methods"]
    end

    subgraph Evaluation["Computational Evaluation"]
        D --> E["<b>Numerical Experiments</b><br/>Evaluate pricing speed and error bounds on European options"]
    end

    E --> F["<b>Key Outcomes</b><br/>• Very fast pricing algorithms<br/>• Full error control<br/>• No retraining needed for new error tolerances"]