{
  "id": "math/0608619",
  "version": "v1",
  "published": "2006-08-24T21:59:56.000Z",
  "updated": "2006-08-24T21:59:56.000Z",
  "title": "Smile Asymptotics II: Models with Known Moment Generating Function",
  "authors": [
    "Shalom Benaim",
    "Peter Friz"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In a recent article the authors obtained a formula which relates explicitly the tail of risk neutral returns with the wing behavior of the Black Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but a moment generating function is available we first establish, under easy-to-check conditions, tail asymptoics on logarithmic scale as soft applications of standard Tauberian theorems. Such asymptotics are enough to make the tail-wing formula work and we so obtain a version of Lee's moment formula with the novel guarantee that there is indeed a limiting slope when plotting implied variance against log-strike. We apply these results to time-changed Levy models and the Heston model. In particular, the term-structure of the wings can be analytically understood.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-08-24T21:59:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E99",
      "91B70"
    ],
    "keywords": [
      "moment generating function",
      "smile asymptotics",
      "scholes implied volatility smile",
      "lees moment formula",
      "black scholes implied volatility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8619B"
    }
  }
}