Pré-Publication, Document De Travail Année : 2025

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

Résumé

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.

Fichier principal
Vignette du fichier
Simulation_Volterra_square_roots-7.pdf (642.89 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-05049978 , version 1 (28-04-2025)

Licence

Identifiants

  • HAL Id : hal-05049978 , version 1

Citer

Eduardo Abi Jaber, Elie Attal. Simulating integrated Volterra square-root processes and Volterra Heston models via Inverse Gaussian. 2025. ⟨hal-05049978⟩
114 Consultations
287 Téléchargements

Partager

  • More