What question did this study set out to answer?

To evaluate European option pricing using a Heston–Hull–White model with deep learning for calibration.

May 13, 2026Mathematics0 citationsOpen Access

European Option Pricing and Deep Learning-Aided Calibration Under Heston–Hull–White with a Stochastic Long-Run Variance Mean

Key Points

To evaluate European option pricing using a Heston–Hull–White model with deep learning for calibration.
Derived a semi-analytical pricing formula using numeraire change and Fourier-transform methods.
Evaluated the model with SSE 50ETF option data from January 2024 to January 2025.
Utilized rolling-window calibration and deep-learning-guided joint calibration scheme.
The proposed model reduced overall pricing errors compared to benchmark models.
Deep learning approach yielded the strongest out-of-sample pricing performance among considered models.

Abstract

This paper studies European option pricing in a Heston–Hull–White model with a stochastic long-run variance mean. Within this setting, a semi-analytical pricing formula is derived using a change of numeraire together with characteristic-function and Fourier-transform methods. The model is examined with SSE 50ETF option data from 1 January 2024 to 1 January 2025 through rolling-window calibration and a deep-learning-guided joint calibration scheme. The empirical results show that the proposed model reduces overall pricing errors relative to several standard benchmark models, while the deep-learning hybrid specification delivers the strongest out-of-sample pricing performance among the models considered.

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