{
  "annotation_id": "1699d05f-fb7d-4df0-b308-c95366409ec1",
  "date_created": "2026-03-02T18:01:00.696000Z",
  "date_modified": "2026-03-02T18:01:00.696000Z",
  "file_hash": "36fe8537b08859f6c1a24cca83272edf3c3d79f0d64e25f263f6c2480c342b97",
  "private": false,
  "record": {
    "abstract": "We apply an asymmetric version of Kirman\u0027s herding model to volatile\nfinancial markets. In the relation between returns and agent concentration we\nuse the square root law proposed by Zhang. This can be derived by extending the\nidea of a critical mean field theory suggested by Plerou et al. We show that\nthis model is equivalent to the so called 3/2-model of stochastic volatility.\nThe description of the unconditional distribution for the absolute returns is\nin good agreement with the DAX independent whether one uses the square root or\na conventional linear relation. Only the statistic of extreme events prefers\nthe former. The description of the autocorrelations are in much better\nagreement for the square root law. The volatility clusters are described by a\nscaling law for the distribution of returns conditional to the value at the\nprevious day in good agreement with the data.",
    "arxiv_id": "physics/0508077",
    "authors": [
      "Friedrich Wagner"
    ],
    "categories": [
      "physics.soc-ph",
      "q-fin.TR"
    ],
    "doi": "10.1016/j.physa.2005.09.070",
    "title": "Application of Zhangs Square Root Law and Herding to Financial Markets",
    "url": "https://arxiv.org/abs/physics/0508077"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d4c1e833-79d0-4d86-b0ca-e1cfd5c79553",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}