{
  "abstract": "Unlike the classical Heston model, Fourier pricing under the rough Heston model requires solving a fractional Riccati equation at every quadrature point. Since the required resolution varies with model parameters and quadrature point, a single uniform time discretization can be inefficient. We develop single- and multilevel Gauss-Laguerre quadrature methods that balance the time discretization and Fourier quadrature errors. Both methods scale the laguerre weight to the estimated Fourier integrand decay. The single-level method allocates a prescribed tolerance between the two errors. The multilevel method splits the integrand into a level-zero term and level differences, selecting quadrature points separately at each level. Suppose that the Fourier integrand discretization error is $O(Δt^p)$, that evaluating the characteristic function once costs $O(Δt^{-β})$, and that the algebraic Gauss-Laguerre quadrature error is $O(N^{-s_{SL}/2})$, where $s_{SL}$ is the smoothness index. Under this estimate and assumptions on the regularity and decay of level differences, we prove that the proposed single-level method requires $O(ε^{-(β/p+2/s_{SL})})$ computational work to achieve accuracy $ε$, whereas the proposed multilevel method requires $O(ε^{-β/p})$ computational work. We also study root-exponential Gauss-Laguerre error models for practical multilevel quadrature allocation. Numerical experiments support the observed fractional Riccati and Fourier integrand convergence rates and root-exponential quadrature behavior, and show substantial reductions in quadrature cost from the proposed scaling. The multilevel method provides clear computational savings over the single-level method. We further benchmark the multilevel fractional Riccati method against the BL2 Markovian approximation and report lower total CPU time in the tested configurations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00438",
  "author_total": 4,
  "authors": [
    {
      "name": "Chiheb Ben Hammouda"
    },
    {
      "name": "Abderrahmene Ben Romdhane"
    },
    {
      "name": "Michael Samet"
    },
    {
      "name": "Raul F. Tempone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8sx4fsxfrq52a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00438",
  "fulltext_url": null,
  "id": "8sx4fsxfrq52a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00438",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "q-fin.CP"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7206198824",
  "pdf_url": "https://arxiv.org/pdf/2609.00438",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8sx4fsxfrq52a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00438",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00438"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Single- and Multilevel Quadrature with Error Control for Fourier Pricing under the Rough Heston Model",
  "title_text": "Single- and Multilevel Quadrature with Error Control for Fourier Pricing under the Rough Heston Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/8sx4fsxfrq52a",
  "venue": "arXiv",
  "versions": []
}