{
  "id": "0911.2992",
  "version": "v3",
  "published": "2009-11-16T09:54:02.000Z",
  "updated": "2010-05-18T07:32:51.000Z",
  "title": "Asymptotic formulae for implied volatility in the Heston model",
  "authors": [
    "Martin Forde",
    "Antoine Jacquier",
    "Aleksandar Mijatovic"
  ],
  "comment": "Presentation in Section 2 has been improved. Theorem 3.1 has been slightly generalised. Figures 2 and 3 now include the at-the-money point.",
  "categories": [
    "q-fin.PR"
  ],
  "abstract": "In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the implied volatility function. The proof is based on saddlepoint methods and classical properties of holomorphic functions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-05-18T07:32:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heston model",
      "asymptotic formulae",
      "large maturity expansion",
      "first order terms",
      "saddlepoint methods"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1098/rspa.2009.0610",
      "journal": "Proceedings of the Royal Society of London Series A",
      "year": 2010,
      "month": "Dec",
      "volume": 466,
      "number": 2124,
      "pages": 3593
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010RSPSA.466.3593F"
    }
  }
}