A NONLINEAR FILTERING APPROACH TO VOLATILITY ESTIMATION WITH A VIEW TOWARDS HIGH FREQUENCY DATA

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  • RÜDIGER FREY
    Swiss Banking Institute, University of Zürich, Plattenstr 14, CH-8032 Zürich, Switzerland
  • WOLFGANG J. RUNGGALDIER
    Dipartimento di Matematica Pura ed Applicata, Universitá di Padova, Via Belzoni 7, I-35131-Padova, Italy

説明

<jats:p> In this paper we consider a nonlinear filtering approach to the estimation of asset price volatility. We are particularly interested in models which are suitable for high frequency data. In order to describe some of the typical features of high frequency data we consider marked point process models for the asset price dynamics. Both jump-intensity and jump-size distribution of this marked point process depend on a hidden state variable which is closely related to asset price volatility. In our setup volatility estimation can therefore be viewed as a nonlinear filtering problem with marked point process observations. We develop efficient recursive methods to compute approximations to the conditional distribution of this state variable using the so-called reference probability approach to nonlinear filtering. </jats:p>

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