Spectral characterization of the quadratic variation of mixed Brownian–fractional Brownian motion

Dzhaparidze and Spreij (Stoch Process Appl, 54:165–174, <CitationRef CitationID="CR5">1994</CitationRef>) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This class contains both semimartingales and non-semimartingales. The motivation comes partially from the recent work by Bender et al. (Finance Stoch, 12:441–468, <CitationRef CitationID="CR2">2008</CitationRef>), where it is shown that the quadratic variation of the log-returns determines the hedging strategy. Copyright Springer Science+Business Media Dordrecht 2013