Convolution-FFT for option pricing in the Heston model

TL;DR

This paper introduces a stable, accurate convolution-FFT method for European option pricing under the Heston model, with explicit error bounds and improved numerical performance over existing Fourier-based techniques.

Contribution

It presents a novel convolution-FFT approach with analytical error bounds for the Heston model, enhancing stability and accuracy in option pricing.

Findings

Stable integrand under large frequency oscillations

Explicit, closed-form error bounds derived

High-accuracy pricing with modest computational cost

Abstract

We propose a convolution-FFT method for pricing European options under the Heston model that leverages a continuously differentiable representation of the joint characteristic function. Unlike existing Fourier-based methods that rely on branch-cut adjustments or empirically tuned damping parameters, our approach yields a stable integrand even under large frequency oscillations. Crucially, we derive fully analytical error bounds that quantify both truncation error and discretization error in terms of model parameters and grid settings. To the best of our knowledge, this is the first work to provide such explicit, closed-form error estimates for an FFT-based convolution method specialized to the Heston model. Numerical experiments confirm the theoretical rates and illustrate robust, high-accuracy option pricing at modest computational cost.