{
  "id": "2308.08760",
  "version": "v1",
  "published": "2023-08-17T03:19:34.000Z",
  "updated": "2023-08-17T03:19:34.000Z",
  "title": "Semi-analytic pricing of American options in some time-dependent jump-diffusion models",
  "authors": [
    "Andrey Itkin"
  ],
  "comment": "18 pages, 1 table, 2 figures",
  "categories": [
    "q-fin.PR",
    "q-fin.CP",
    "q-fin.MF"
  ],
  "abstract": "In this paper we propose a semi-analytic approach to pricing American options for some time-dependent jump-diffusions models. The idea of the method is to further generalize our approach developed for pricing barrier, [Itkin et al., 2021], and American, [Carr and Itkin, 2021; Itkin and Muravey, 2023], options in various time-dependent one factor and even stochastic volatility models. Our approach i) allows arbitrary dependencies of the model parameters on time; ii) reduces solution of the pricing problem for American options to a simpler problem of solving an algebraic nonlinear equation for the exercise boundary and a linear Fredholm-Volterra equation for the the option price; iii) the options Greeks solve a similar Fredholm-Volterra linear equation obtained by just differentiating Eq. (25) by the required parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-17T03:19:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "american options",
      "time-dependent jump-diffusion models",
      "semi-analytic pricing",
      "similar fredholm-volterra linear equation",
      "stochastic volatility models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}