{
  "id": "math/0603146",
  "version": "v2",
  "published": "2006-03-06T17:33:32.000Z",
  "updated": "2006-03-07T00:13:58.000Z",
  "title": "Regular Variation and Smile Asymptotics",
  "authors": [
    "Shalom Benaim",
    "Peter Friz"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the ideal mathematical framework to formulate and prove such results. The practical value of our formulae comes from the vast literature on tail asymptotics and our conditions are often seen to be true by simple inspection of known results.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-03-07T00:13:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E99",
      "91B70"
    ],
    "keywords": [
      "regular variation",
      "smile asymptotics",
      "roger lees celebrated moment formula",
      "sharpening roger lees celebrated moment",
      "tail asymptotics translate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3146B"
    }
  }
}