A bounded and periodic interest rate model

dc.contributorLee, Junsoo
dc.contributorMai, Tsun-Zee
dc.contributorTrent, Tavan T.
dc.contributorWu, Zhijian
dc.contributor.advisorWang, Pu
dc.contributor.authorCai, Chen
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2017-03-01T16:47:09Z
dc.date.available2017-03-01T16:47:09Z
dc.date.issued2013
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractIn financial market, interest rate is crucially important. Its changes and moves have a great impact on consumer's products, inflation rate, bond and stock market, and almost all the aspects in the financial world. An ideal stochastic model describing the volatility of the short-term interest rate would possess the following nice properties. First it has to have the periodic behavior; this is different from stock price model in which it has an increasing or decreasing trends. Second, it should maintain in a positive range and be bounded. Third, its differential equation should be simple and have an analytical solution so that its density function as well as any moments can be readily derived. In this dissertation, we propose and investigate such a stochastic differential equation. Its solution involves sine/cosine wave functions of Brownian motion that has all these properties. Their statistical properties such as mean, variance and covariance structure of this interest rate at any time are derived; their relation with martingale is established; both analytical and numerical solutions are obtained. From this interest rate model, the term structures and the yield curves will also be demonstrated for various settings.en_US
dc.format.extent65 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0001222
dc.identifier.otherCai_alatus_0004D_11516
dc.identifier.urihttps://ir.ua.edu/handle/123456789/1694
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.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectMathematics
dc.titleA bounded and periodic interest rate modelen_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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