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

TL;DR

This paper extends the approximation of quadratic variation via randomized periodograms to a broader class of continuous stochastic processes, including both semimartingales and non-semimartingales, with implications for financial hedging strategies.

Contribution

It demonstrates that the randomized periodogram approximation applies to a new class of processes, expanding the understanding of quadratic variation estimation.

Findings

Approximation valid for a wider class of processes

Includes both semimartingales and non-semimartingales

Implications for financial hedging strategies

Abstract

Dzhaparidze and Spreij [5] 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. [2], where it is shown that the quadratic variation of the log-returns determines the hedging strategy.