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Complex discontinuities of $\surd\overline{\text{Fredholm determinants}}$ in the Volterra Stein-Stein model

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  • Eduardo Abi Jaber
  • Maxime Guellil

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.

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  • Eduardo Abi Jaber & Maxime Guellil, 2025. "Complex discontinuities of $\surd\overline{\text{Fredholm determinants}}$ in the Volterra Stein-Stein model," Papers 2503.02965, arXiv.org.
    • Handle: RePEc:arx:papers:2503.02965
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