# A bounded and periodic interest rate model

 dc.contributor Lee, Junsoo dc.contributor Mai, Tsun-Zee dc.contributor Trent, Tavan T. dc.contributor Wu, Zhijian dc.contributor.advisor Wang, Pu dc.contributor.author Cai, Chen dc.date.accessioned 2017-03-01T16:47:09Z dc.date.available 2017-03-01T16:47:09Z dc.date.issued 2013 dc.identifier.other u0015_0000001_0001222 dc.identifier.other Cai_alatus_0004D_11516 dc.identifier.uri https://ir.ua.edu/handle/123456789/1694 dc.description Electronic Thesis or Dissertation dc.description.abstract In 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. dc.format.extent 65 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.ispartof The University of Alabama Libraries Digital Collections dc.relation.hasversion born digital dc.rights All rights reserved by the author unless otherwise indicated. dc.subject.other Mathematics dc.title A bounded and periodic interest rate model 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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