SWIFT calibration of the Heston model

TL;DR

This paper extends the SWIFT method for efficient calibration of the Heston model, leveraging closed-form characteristic functions to achieve fast and reliable option pricing across various market conditions.

Contribution

It introduces a novel calibration approach that significantly speeds up Heston model fitting using SWIFT, with practical implementation advantages and extensive numerical validation.

Findings

Calibration is extremely fast for single expiry and multiple strikes.

The method outperforms existing state-of-the-art calibration techniques.

Numerical experiments demonstrate robustness across diverse options and maturities.

Abstract

In the present work, the European option pricing SWIFT method is extended for Heston model calibration. The computation of the option price gradient is simplified thanks to the knowledge of the characteristic function in closed form. The proposed calibration machinery appears to be extremely fast, in particular for a single expiry and multiples strikes, outperforming the state-of-the-art method we compare with. Further, the a priori knowledge of SWIFT parameters makes possible a reliable and practical implementation of the presented calibration method. A wide set of stress, speed and convergence numerical experiments is carried out, with deep in-the-money, at-the-money and deep out-of-the-money options for very short and very long maturities.