Stochastic volatility and fractional Brownian motion

A. Gloter and Marc Hoffmann ()

Stochastic Processes and their Applications, 2004, vol. 113, issue 1, 143-172

Abstract: We observe (Yt) at times i/n, i=0,...,n, in the parametric stochastic volatility modeldYt=[Phi]([theta],WtH) dWt,where (Wt) is a Brownian motion, independent of the fractional Brownian motion (WtH) with Hurst parameter . The sample size n increases not because of a longer observation period, but rather, because of more frequent observations. We prove that the unusual rate n-1/(4H+2) is asymptotically optimal for estimating the one-dimensional parameter [theta], and we construct a contrast estimator based on an approximation of a suitably normalized quadratic variation that achieves the optimal rate.

Keywords: Stochastic; volatility; models; Discrete; samplings; High-frequency; data; Fractional; Brownian; motion; Contrast; estimators (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (8)

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