Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2025

Complex discontinuities of the square root of Fredholm determinants in the Volterra Stein-Stein model

Résumé

We study complex discontinuities arising from the miscomputation of the Fourier-Laplace transform in the Volterra Stein-Stein model, which involves the complex square root of a Fredholm determinant. Discontinuities occur when the determinant crosses the negative real axis. We characterize these crossings for the joint Fourier-Laplace transform of the integrated variance and log-price. Additionally, we derive a corrected formula for the Fourier-Laplace transform and develop efficient numerical techniques to detect and compute these crossings. Applying our algorithms to Fourier-based pricing in the rough Stein-Stein model, we achieve a significant increase in accuracy while drastically reducing computational cost compared to existing methods.

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Dates et versions

hal-04977771 , version 1 (05-03-2025)
hal-04977771 , version 2 (16-11-2025)

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  • HAL Id : hal-04977771 , version 1

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Eduardo Abi Jaber, Maxime Guellil. Complex discontinuities of the square root of Fredholm determinants in the Volterra Stein-Stein model. 2025. ⟨hal-04977771v1⟩
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