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Volatility analysis for high frequency financial data

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dc.contributorBelbas, Stavros Apostol
dc.contributorEvans, Martin J.
dc.contributorNeggers, Joseph
dc.contributorWu, Zhijian
dc.contributorZhang, Jingyuan
dc.contributor.advisorWu, Zhijian
dc.contributor.authorZheng, Xiaohua
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2017-02-28T22:20:49Z
dc.date.available2017-02-28T22:20:49Z
dc.date.issued2009
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractMeasuring 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.en_US
dc.format.extent79 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0000070
dc.identifier.otherZHENG_alatus_0004D_10089
dc.identifier.urihttps://ir.ua.edu/handle/123456789/577
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectMathematics
dc.titleVolatility analysis for high frequency financial dataen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Mathematics
etdms.degree.disciplineMathematics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.

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