{
  "abstract": "This paper develops a non-local mesh-free framework for pricing European options under the Heston stochastic volatility model, addressing the challenges of strong negative correlation and diffusion degeneracy near the zero-variance boundary. The method employs a state-dependent adaptive horizon that refines non-local interactions near the degenerate boundary while relaxing them in the interior and enforces sign-restricted coefficients to ensure a discrete maximum principle and monotonicity in option values. For time-stepping, an implicit–explicit second-order backward differentiation scheme is used, with a Rannacher startup procedure to dampen transient oscillations from the non-smooth pay-off at the strike. Numerical comparisons against a modified Craig–Sneyd alternating-direction implicit solver confirm comparable accuracy and approximately second-order convergence, with the method maintaining close agreement in stressed regimes of high negative correlation and severe variance degeneracy. Despite higher computational costs, the framework offers greater flexibility on non-uniform point sets and robust performance near degenerate boundaries, making it particularly attractive for adaptive pricing applications involving irregular cash-flow structures or localized resolution around critical exercise regions.",
  "abstract_shown": true,
  "affiliations": [
    "School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521000, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Dan Qu"
    },
    {
      "affs": [
        0
      ],
      "name": "Yanbo Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/535hy2z587kqn.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193585",
  "fulltext_url": null,
  "id": "535hy2z587kqn",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3585",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7216427327",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/535hy2z587kqn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193585",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3585"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "A Degeneracy-Aligned and Discrete Maximum-Principle- Compatible Peridynamic Differential Operator for the Heston Stochastic Volatility Model",
  "title_text": "A Degeneracy-Aligned and Discrete Maximum-Principle- Compatible Peridynamic Differential Operator for the Heston Stochastic Volatility Model",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/535hy2z587kqn",
  "venue": "Mathematics",
  "versions": []
}