{
  "id": "cond-mat/0101474",
  "version": "v1",
  "published": "2001-01-31T18:51:23.000Z",
  "updated": "2001-01-31T18:51:23.000Z",
  "title": "Numerical analysis of the Minimal and Two-Liquid models of the Market Microstructure",
  "authors": [
    "David L. C. Chan",
    "David Eliezer",
    "Ian I. Kogan"
  ],
  "comment": "69 pages, 50 figures, Latex",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We present results of numerical analysis of several simple models for the microstructure of a double auction market without intermediaries which were introduced in cond-mat/9808240. We perform computer simulations of the minimal model in order to verify liquidity scaling laws. A logarithmic correction to the scaling law for midmarket variance is observed, but not for bid-offer spread or its fluctuation, because they are fundamentally different quantities. Time to midmarket sale ($\\tau_S$) is found to scale as 1/J while its fluctuation goes as $0.73/J$. A ``reduced'' time ($\\tau_{reduced}$) is also studied, and found to scale in a non-trivial way. Asymmetric fluxes are introduced to the minimal model and analytical result derived earlier for the speed of the moving midmarket agrees with numerical results. Simulation of the two-liquid model which describes a market with both market order and limit order traders, reveals widening of the bid-offer spread when the flux of market order traders exceeds that of limit order traders. The variation of the spread with the fraction of market-order traders is investigated. The formula for asymmetric fluxes is applied to the two-liquid model and its predictions are found to agree with experiment. The critical point is approximately determined, and the ratio of the midmarkets for $f = 0.0$ and $f = 0.5$ (where $f$ is the fraction of market-order traders) is calculated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-01-31T18:51:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-liquid model",
      "numerical analysis",
      "market microstructure",
      "limit order traders",
      "market order traders exceeds"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 69,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001cond.mat..1474C"
    }
  }
}