Volatility analysis for high frequency financial data

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dc.contributor Belbas, Stavros Apostol
dc.contributor Evans, Martin J.
dc.contributor Neggers, Joseph
dc.contributor Wu, Zhijian
dc.contributor Zhang, Jingyuan
dc.contributor.advisor Wu, Zhijian
dc.contributor.author Zheng, Xiaohua
dc.date.accessioned 2017-02-28T22:20:49Z
dc.date.available 2017-02-28T22:20:49Z
dc.date.issued 2009
dc.identifier.other u0015_0000001_0000070
dc.identifier.other ZHENG_alatus_0004D_10089
dc.identifier.uri https://ir.ua.edu/handle/123456789/577
dc.description Electronic Thesis or Dissertation
dc.description.abstract Measuring and modeling financial volatility are key steps for derivative pricing and risk management. In financial markets, there are two kinds of data: low-frequency financial data and high-frequency financial data. Most research has been done based on low-frequency data. In this dissertation we focus on high-frequency data. In theory, the sum of squares of log returns sampled at high frequency estimates their variance. For log price data following a diffusion process without noise, the realized volatility converges to its quadratic variation. When log price data contain market microstructure noise, the realized volatility explodes as the sampling interval converges to 0. In this dissertation, we generalize the fundamental Ito isometry and analyze the speed with which stochastic processes approach to their quadratic variations. We determine the difference between realized volatility and quadratic variation under mean square constraints for Brownian motion and general case. We improve the estimation for quadratic variation. The estimators found by us converge to quadratic variation at a higher rate.
dc.format.extent 79 p.
dc.format.medium electronic
dc.format.mimetype application/pdf
dc.language English
dc.language.iso en_US
dc.publisher University of Alabama Libraries
dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations
dc.relation.hasversion born digital
dc.rights All rights reserved by the author unless otherwise indicated.
dc.subject.other Mathematics
dc.title Volatility analysis for high frequency financial data
dc.type thesis
dc.type text
etdms.degree.department University of Alabama. Dept. of Mathematics
etdms.degree.discipline Mathematics
etdms.degree.grantor The University of Alabama
etdms.degree.level doctoral
etdms.degree.name Ph.D.

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