{
  "id": "1403.7387",
  "version": "v1",
  "published": "2014-03-28T14:28:11.000Z",
  "updated": "2014-03-28T14:28:11.000Z",
  "title": "Multi-scaling of moments in stochastic volatility models",
  "authors": [
    "Paolo Dai Pra",
    "Paolo Pigato"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a class of stochastic volatility models $(X_t)_{t \\geq 0}$ for which the absolute moments of the increments exhibit anomalous scaling: $\\E\\left(|X_{t+h} - X_t|^q \\right)$ scales as $h^{q/2}$ for $q < q^*$, but as $h^{A(q)}$ with $A(q) < q/2$ for $q > q^*$, for some threshold $q^*$. This multi-scaling phenomenon is observed in time series of financial assets. If the dynamics of the volatility is given by a mean-reverting equation driven by a Levy subordinator and the characteristic measure of the Levy process has power law tails, then multi-scaling occurs if and only if the mean reversion is superlinear.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-28T14:28:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G44",
      "91B25",
      "91G70"
    ],
    "keywords": [
      "stochastic volatility models",
      "multi-scaling",
      "power law tails",
      "absolute moments",
      "mean-reverting equation driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7387P"
    }
  }
}