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

Eduardo Abi Jaber () and Maxime Guellil ()
Additional contact information
Eduardo Abi Jaber: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Maxime Guellil: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité

Working Papers from HAL

Abstract: 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.

Keywords: Volterra Stein-Stein model; Fredholm determinant; Fourier-Laplace transform; Complex discontinuities; Fourier pricing; Mathematics Subject Classification (2020): 91G20; 45P05 (search for similar items in EconPapers)
Date: 2025-03-04
Note: View the original document on HAL open archive server: https://hal.science/hal-04977771v1
References: Add references at CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-04977771v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-04977771

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().