{
  "annotation_id": "d5e66b7e-ec25-4ee9-a434-3324724b4532",
  "date_created": "2026-02-17T05:53:20.412000Z",
  "date_modified": "2026-02-17T05:53:20.412000Z",
  "file_hash": "e63167da7710f542e059ad71725c765ad5ff911e724850d94863252cbdad699a",
  "private": false,
  "record": {
    "abstract": "In this paper we study the Fourier estimator of Malliavin and Mancino for the spot volatility. We establish the convergence of the trigonometric polynomial to the volatility\u0027s path in a setting that includes the following aspects. First, the volatility is required to satisfy a mild integrability condition, but otherwise allowed to be unbounded. Second, the price process is assumed to have cadlag paths, not necessarily continuous. We obtain convergence rates for the probability of a bad approximation in estimated coefficients, with a speed that allow to obtain an almost sure convergence and not just in probability in the estimated reconstruction of the volatility\u0027s path. This is a new result even in the setting of continuous paths. We prove that a rescaled trigonometric polynomial approximate the quadratic jump process.",
    "arxiv_id": "2601.09074",
    "authors": [
      "L. J. Espinosa Gonz\u00e1lez",
      "Erick Trevi\u00f1o Aguilar"
    ],
    "categories": [
      "q-fin.CP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "title": "The Fourier estimator of spot volatility: Unbounded coefficients and jumps in the price process",
    "url": "https://arxiv.org/abs/2601.09074",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "734b70cd-d5d7-4d4d-b516-5eeea0b44e96",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}