An important application of term structure models is to measure the difference between the evolutions of two yield curves starting from the same initial point. Such a geometric problem can be tackled by use of the notion of information geometry after the mapping of yield curves to density functions on a Hilbert space. We prove that a pair of yield curves with large initial Bhattacharyya spherical distance would diverge from each other with a significant probability. / Finally, we implement the proposed model with initial data in the US swap market for 15 Feb, 2007. To test our model improvements over the traditional models, we also run the simulation with the Hull-White model and compare these two no-arbitrage models in various major characteristics. It shows that the proposed model forms a bridge linking interest rates and discount bonds, namely, given the initial term structure density and the volatility structure, we are able to reconstruct the short rate process and the bond price process. Our term structure density model is thus a unification of traditional models each having its own advantage. / Following the initial study of Brody and Hughston on applying information geometry to interest rate modeling, we propose a novel term structure model and investigate its application in the US swap market. Different from the traditional term structure models that impose assumptions on either bonds or rates, the newly proposed model is characterized by the evolution of a density function which is obtained from the derivative of the discount function with respect to the time left till maturity. We prove that such a density function can be interpreted as interest return on the discount bond. / The introduction of the term structure density turns the problem of yield curve dynamics into a problem of the evolution of a density distribution. There are at least three steps to model the dynamics of the density function: calibrate the initial term structure density, specify the market risk premium, and choose a proper volatility structure. First, we introduce two initial calibration methods, one by maximizing the Tsallis entropy and the other by the notion of superstatistics. By use of either method, we deduce a power-law distribution for the initial term structure density function. The entropy index q in this function, which is a well-known physics quantity, now finds its financial interpretation as the measure of departure of the current term structure from flatness on a continuously compounded basis. Our empirical experiments in the US swap market fully demonstrate this observation. Next, given the calibrated initial density, we develop the term structure dynamics in the risk-neutral world and prove that the market risk premium is immaterial. To deduce a concise martingale representation for the bond pricing formula, we choose a density volatility that possesses zero mean. Finally, as an illustration of the importance of volatility structure, the HJM volatilities are redesigned for interest rate positivity under the framework of the current model. / Yang, Yiping. / Adviser: Kwong Chung Ping. / Source: Dissertation Abstracts International, Volume: 73-03, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 187-192). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.