{
  "id": "0707.1243",
  "version": "v1",
  "published": "2007-07-09T12:39:10.000Z",
  "updated": "2007-07-09T12:39:10.000Z",
  "title": "Euler Scheme and Tempered Distributuions",
  "authors": [
    "Julien Guyon"
  ],
  "comment": "26 pages",
  "journal": "Stochastic Processes and their Applications 116, 6 (2006) 877-904",
  "categories": [
    "math.PR"
  ],
  "abstract": "Given a smooth R^d-valued diffusion, we study how fast the Euler scheme with time step 1/n converges in law. To be precise, we look for which class of test functions f the approximate expectation E[f(X^{n,x}_1)] converges with speed 1/n to E[f(X^x_1)]. If X is uniformly elliptic, we show that this class contains all tempered distributions, and all measurable functions with exponential growth. We give applications to option pricing and hedging, proving numerical convergence rates for prices, deltas and gammas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-09T12:39:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60J60",
      "60H35",
      "65M15",
      "65C05",
      "65C20",
      "65B05"
    ],
    "keywords": [
      "euler scheme",
      "tempered distributuions",
      "approximate expectation",
      "time step",
      "class contains"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.1243G"
    }
  }
}