{
  "abstract": "We derive a first-order representation of Black-Scholes implied variance in a continuous local martingale model. Total implied variance is the conditional expectation of the quadratic variation of the log price given its terminal value, up to a smaller-order term, for bounded standardized log-strikes. The framework incorporates small volatility-of-volatility, fast mean-reverting, and short-maturity asymptotics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13961",
  "author_total": 1,
  "authors": [
    {
      "name": "Masaaki Fukasawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c0vhx3dyvftyh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13961",
  "fulltext_url": null,
  "id": "c0vhx3dyvftyh",
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  "landing_url": "https://arxiv.org/abs/2609.13961",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "q-fin.MF"
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      "arxiv",
      "q-fin.PR"
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.13961",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c0vhx3dyvftyh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13961",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13961"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Yet another asymptotic formula for implied volatility",
  "title_text": "Yet another asymptotic formula for implied volatility",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/c0vhx3dyvftyh",
  "venue": "arXiv",
  "versions": []
}