{
  "abstract": "Closed-form multi-asset first-passage prices become rare once dependence is allowed to vary with the state. We build a two-asset local-volatility/local-correlation family in which relative-performance passage problems stay one-dimensional by construction. Under a common instantaneous volatility, the log-ratio and log-product are orthogonal, and their variance rates form a simple budget. Holding the variance rate of the log-ratio fixed while leaving the orthogonal index variance free produces the Brownian-dispersion model: the log-ratio is an exact Brownian motion under the pricing measure, whereas the geometric-mean index carries the state-dependent volatility and correlation. Cash-settled and one-homogeneous claims whose path dependence is carried by the ratio are then invariant to the local-correlation specification; the second property holds more generally under constant relative variance, while the first is specific to the orthogonal design. We derive double-knock-out exchange-option, cash-rebate and relative-performance lookback formulas and identify an index-dependent subclass in which ratio and index are independent. There, a two-dimensional exit law factorises and an exchange option knocked out on a curvilinear region is priced as a ratio double-knock-out value times a one-dimensional index survival probability. Simulations under sharply different local-correlation functions confirm the invariant prices while generating very different fixed-strike basket prices.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Statistical and Actuarial Sciences, Western University, London, ON N6A 5B7, Canada"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Marcos Escobar-Anel",
      "orcid": "0000-0001-9691-4322"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ekese1jn9ra7.bib",
  "cited_by": 0,
  "doi": "10.3390/math14213895",
  "fulltext_url": null,
  "id": "0ekese1jn9ra7",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/3895",
  "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": "W7223651206",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/0ekese1jn9ra7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14213895",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/3895"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Designed Dependence for Tractable Two-Asset First-Passage Pricing",
  "title_text": "Designed Dependence for Tractable Two-Asset First-Passage Pricing",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/0ekese1jn9ra7",
  "venue": "Mathematics",
  "versions": []
}