Stochastic volatility and fractional Brownian motion
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.
Year of publication: |
2004
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Authors: | Gloter, A. ; Hoffmann, M. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 113.2004, 1, p. 143-172
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Publisher: |
Elsevier |
Keywords: | Stochastic volatility models Discrete samplings High-frequency data Fractional Brownian motion Contrast estimators |
Saved in:
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