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Simulating integrated Volterra square-root processes and Volterra Heston models via Inverse Gaussian

Author

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  • 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)

  • Elie Attal

    (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)

Abstract

We introduce a novel simulation scheme, iVi (integrated Volterra implicit), for integrated Volterra square-root processes and Volterra Heston models based on the Inverse Gaussian distribution. The scheme is designed to handle $L^1$ kernels with singularities by relying solely on integrated kernel quantities, and it preserves the non-decreasing property of the integrated process. We establish weak convergence of the iVi scheme by reformulating it as a stochastic Volterra equation with a measure kernel and proving a stability result for this class of equations. Numerical results demonstrate that convergence is achieved with very few time steps. Remarkably, for the rough fractional kernel, unlike existing schemes, convergence seems to improve as the Hurst index H decreases and approaches -1/2.

Suggested Citation

  • Eduardo Abi Jaber & Elie Attal, 2025. "Simulating integrated Volterra square-root processes and Volterra Heston models via Inverse Gaussian," Working Papers hal-05049978, HAL.
    • Handle: RePEc:hal:wpaper:hal-05049978
    Note: View the original document on HAL open archive server: https://hal.science/hal-05049978v1
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