{
  "id": "1610.03230",
  "version": "v1",
  "published": "2016-10-11T08:10:45.000Z",
  "updated": "2016-10-11T08:10:45.000Z",
  "title": "Barrier Option Pricing under the 2-Hypergeometric Stochastic Volatility Model",
  "authors": [
    "Rúben Sousa",
    "Ana Bela Cruzeiro",
    "Manuel Guerra"
  ],
  "comment": "18 pages",
  "categories": [
    "math.PR",
    "q-fin.MF",
    "q-fin.PR"
  ],
  "abstract": "The purpose of this work is to investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model which has recently been introduced as an attempt to tackle one of the most serious shortcomings of the famous Black and Scholes option pricing model: the fact that it does not reproduce the volatility smile and skew effects which are commonly seen in observed price data from option markets. After a review of the basic theory of option pricing under stochastic volatility, we employ the regular perturbation method from asymptotic analysis of partial differential equations to derive an explicit and easily computable approximate formula for the pricing of barrier options under the 2-hypergeometric stochastic volatility model. The asymptotic convergence of the method is proved under appropriate regularity conditions, and a multi-stage method for improving the quality of the approximation is discussed. Numerical examples are also provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-11T08:10:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "91G20",
      "91B25",
      "60H30",
      "35C20"
    ],
    "keywords": [
      "stochastic volatility model",
      "barrier option pricing",
      "regular perturbation method",
      "scholes option pricing model",
      "partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}