A bounded and periodic interest rate model

Thumbnail Image
Journal Title
Journal ISSN
Volume Title
University of Alabama Libraries

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.

Electronic Thesis or Dissertation