{
  "abstract": "We develop semi-closed pricing formulas and lifted-model hedging methods for discretely monitored geometric and arithmetic Asian options in the Volterra-Heston stochastic volatility model. Exploiting the affine Volterra structure, we derive a tractable transform for the joint law of the terminal log-price and the discretely monitored geometric average. This transform yields semi-closed pricing formulas for geometric Asian options, which in turn provide effective control variates for Monte Carlo valuation of arithmetic Asian options. Under the stated real-moment and affine-transform hypotheses, we also derive the Galtchouk-Kunita-Watanabe decomposition for Fourier-representable payoffs and obtain a variance-optimal hedge in terms of the Riccati-Volterra equation and the forward-variance curve. Using N-factor Markovian approximations, we obtain a finite-dimensional numerical implementation for hedging Asian options. Our numerical experiments document factor convergence for a regular non-Markovian kernel and the effect of rebalancing frequency on hedging error. In the Heston benchmark, geometric Asian controls substantially reduce the variance of arithmetic-Asian price estimates and improve the finite-sample stability of regression-based hedging relative to direct regression.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07169",
  "author_total": 3,
  "authors": [
    {
      "name": "Gijs Custers"
    },
    {
      "name": "Sven Karbach"
    },
    {
      "name": "Martin Friesen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cmnpq517j4cg8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07169",
  "fulltext_url": null,
  "id": "cmnpq517j4cg8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07169",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "q-fin.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7212015493",
  "pdf_url": "https://arxiv.org/pdf/2609.07169",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cmnpq517j4cg8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07169",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07169"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Pricing and Hedging of Discretely Monitored Asian Options in the Volterra-Heston Model",
  "title_text": "Pricing and Hedging of Discretely Monitored Asian Options in the Volterra-Heston Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/cmnpq517j4cg8",
  "venue": "arXiv",
  "versions": []
}