Enhancing Fourier pricing with machine learning

TL;DR

This paper introduces a machine learning approach to optimize tuning parameters in Fourier pricing methods for European options, enabling fast, accurate pricing with adjustable error control without retraining.

Contribution

It proposes learning Fourier method tuning parameters via machine learning, allowing flexible, error-controlled option pricing without retraining for different tolerances.

Findings

Achieves fast option pricing with full error control.

Works with any error tolerance without retraining.

Demonstrates effectiveness using the Heston model.

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.