Modeling The Term Structure Of Interest Rate In Fixed Income Market With Applications

Modeling term structure of interest rate with applications mainly include research on traditional theory of term structure of interest rate, generalized equilibrium models of term structure of interest rate, no-arbitrage models of term structure of interest rate and interest rate risk measuring and management.There are expectation theory, market segmentation theory and liquidity preference theory in classical traditional theory of term structure of interest rate. According to China's government bond repo rate data, the dissertation individually utilizes unit root method, co-integration analysis method, vector error correction model and factor decomposition procedure to empirically examine expectation hypothesis based on liquidity preference premium. And the result shows that there is only a common stochastic trend which drives interest rate system composed of each bond repo rate, the forecast ability of interest rate spread is correlated with degree of volatility of interest rate and is significantly strengthened for transitory component of future short term interest rate when the permanent component is removed from short term interest rate series, but gets weak predictive power for the permanent component.Under generalized equilibrium framework of term structure of interest rate models, the dissertation, on the one hand, proposes extended bootstrap method by integrating traditional bootstrap method and cubic spline method and avoids introducing additional equations when utilizing extended bootstrap method by directly designing the function form of term structure of interest rate model. In the meanwhile, the empirical results indicate that the proposed model can capture complicated shape of yield curve and predict future interest rate change. On the other hand, following general CKLS'modeling ideas, the dissertation optimally estimate five different short term interest rate models by adopting GMM and MLE methods, compares these models'descriptive power for the interest rate change behavior by utilizing the log likelihood ratio and Vuong test statistics, corrects the bias of initial parameter values of model by indirect inference method and applies the parameter value of optimal model to the Changjiang River Power Corporation's warrant (CWB1) assuming interest rate's stochastic behavior.Under Heath-Jarrow-Morton framework of term structure of interest rate models, the dissertation derives the no-arbitrage drift term restriction of dynamics of forward interest rate and decomposes forward interest rate term structure into two component functions by a new decomposition technique. According to the procedure, the dissertation also empirically investigates the ability for the model to fit the forward interest rate term structure with the sample of 58 weekly bond price data of Shanghai Stock Exchange. The results show that the three-factor HJM specification has stable exponential decay structure and is a consistent representation of the term structure of interest rate during the sampling period.Based on analyzing the inherent relation between the volatility structure and the dynamics of forward interest rate, the dissertation presents Markovian framework for HJM class models, investigates the topics for introducing stochastic jump component into pure diffusion process under HJM and Markovian system transformation and reduction for different forward rate volatility specification, and simulates the initial bond and bond option price for deterministic and state dependent volatility structure by utilizing Monte Carlo method based on control variate technique.Under HJM framework, the dissertation generalizes traditional duration and convexity measure to generalized stochastic duration and convexity for accurately measuring interest rate risk by choosing a zero-coupon bond yield for an arbitrary maturity as state variable, and analyzes interest risk immunization of bonds portfolio for single and two factor HJM models. Finally, the dissertation empirically computes traditional duration and convexity as well as generalized stochastic duration and convexity based on three different forward rate volatility specifications.