Research On Term Structure Of Interest Rates With Applications

The theories and models on term structure of interest rates are one of the most challenging works in finance research and an important fundamental branch in fixed income and financial engineering field. The aim of the dissertation is to review recent twenty years' evolving process of theories on term structure of interest rates, analyze classical models of term structure of interest rates under general equilibrium and no-arbitrage frames and finally apply them to the two fields of modern finance theory: pricing of interest rates derivatives and management and control of interest rates risk. The dissertation firstly divided the theories on term structure of interest rates into four phases, briefly introduced classical modes and corresponding empirical studies, put forward the modeling process of interest rates and appraisal standard, and discussed the recent advancement in this field. Then, on the basis of studying the mechanism and influential factors of term structure of Treasury bond, the dissertation extended traditional bootstrapping method and estimated government bonds yield curve with Chinese government bonds quoted price, by employing cubic spline interpolation method, and hence, established the static term structure of interest rates of Chinese government bonds. As for the dynamic study of term structure of interest rates, the dissertation divided the models into equilibrium models and no-arbitrage models according to the study frame of stochastic term structure of interest rates, where the former includes one-factor models such as Merton, Vasicek, CIR models and multi-factors models such as Brennan-Schwartz, Fong-Vasicek, Longstaff-Schwartz models, the latter include Ho-Lee, Hull-White, BDT and HJM class models. The dissertation also discusses the criteria for choosing the appropriate term structure of interest rates. As for the application of term structure of interest rates, the thesis firstly introduced the types and pricing methods of interest rates derivatives, discussed the equivalence of PDE and Martingale methods, and established the multi-steps binomial tree models of government bonds and the two factors models of convertible bonds. Then the thesis introduced interest rates risk, duration and convex measures and interest rates management policies and principles, analyzed interest rates risk immunity strategies according to the change scope of the yield curve, and finally designed bond immunity portfolio under the HJM frames of stochastic term structure of interest rates.