Theories, Models And Applications Of The Term Structure Of Interest Rates

The term structure of interest rates reflects the influence of the time factor on interest rates, that is the market's expectations of future interest rates given the current market conditions, which makes it the benchmark for the entire financial system and the basis for asset pricing and hedging, and thus the key to interpret the effect of the monetary policy and its transmission mechanism. So research on the term structure of interest rates is the fundamental work of critical importance in the financial engineering field.In this dissertation, a systematic and intensive study is made on theories, models and applications of the term structure of interest rates from six aspects below respectively: formation mechanism theories of term structure of interest rates, static term structure models of interest rates, generalized equilibrium models of term structure of interest rates, no-arbitrage models of term structure of interest rates, HJM framework of defaultable term structure models and estimation theories for term structure models.First, based on a concise introduction to formation mechanism theories of term structure of interest rates, an empirical research is made on the applicability of the expectation hypothesis (EH) to different parts of the term structure of SHIBOR using the unit root test and cointegration method, which results in the find that EH is not applicable to the whole yield curve of SHIBOR. However, EH works on the short and long parts of the SHIBOR term structure respectively. Thus, vector error correction models are established to investigate the effect of the monetary policy on the yield curve and it is found that the effect tends to decline along the term structure of SHIBOR, which means that monetary policy transmission in SHIBOR market need further improvements. Furthermore, the result of principal component analysis indicates that the dynamics of the term structure of SHIBOR can be captured by three main factors, that is the level factor, the slope factor and the curvature factor.Second, based on a brief introduction to static term structure models of interest rates, an estimation approach based on the genetic algorithm (hereafter GA) is introduced for the extended Nelson-Siegel model to improve its fitness. Then an empirical comparison is made between the bootstrap method based on cubic spline interpolation, the extended Nelson-Siegel model based on nonlinear regression and the model introduced above. Then yield curves are estimated based on the method proposed for the three sample dates and the influence of the financial crisis and monetary policy on the curve is analyzed.Third, based on a systematic introduction to the generalized equilibrium framework of term structure models of interest rates, intensive research is made on equilibrium models from the aspects of estimation methods, applicability and regime switching respectively. Firstly, in the CKLS general framework, the dissertation introduces approaches of estimation for equilibrium models of term structure of interest rates based on EKF and UKF, and an empirical contrast is made between the estimation performances of the EKF-based and UKF-based algorithms. Furthermore, the fitness of Vasicek model and CIR model is compared with both the foreign and domestic data using the UKF-based algorithm. Finally, under a RSCIR model, an empirical research is carried out on the dynamics of the term structure and risk premium of SHIBOR using the Kim filter based maximum likelihood estimator, with especial attention given to the regime-switching characteristic of the SHIBOR evolution and the corresponding market implications, and a comparison is also made between RSCIR model and CIR model based on the SHIBOR data above.Fourth, based on an in-depth study on the HJM framework of no-arbitrage models, the dissertation performs finite-dimensional Markovian affine realization for HJM models under a certain volatility specification, based on which a direct estimation method and a maximum likelihood estimator based on the unscented Kalman filter are introduced for HJM models in two different ways. Finally empirical research is made on the SHIBOR term structure based on the two estimation methods above respectively, which comes to a conclusion that the dynamics and volatility structure of SHIBOR are both well captured by a three-factor HJM model, and the level and slope factors explain the majority of the variation of the yield curve.Fifth, Heath-Jarrow-Morton model is generalized by extending the no-arbitrage drift restriction with nonzero instantaneous correlations between volatility factors and setting forward rate volatilities subject to generalized mean-reverting square-root processes and correlated with innovations to forward rates. Then a quasi-analytical formula for zero coupon bond prices is derived based on the finite-dimensional Markovian affine realization of the model framework above.Finally, a stochastic volatility HJM framework of defaultable term structure models is proposed by introducing stochastic volatility process into the defaultable HJM framework. Then finite-dimensional Markovian affine realization is performed for the model framework established above under a certain volatility specification, based on which a explicit analytical pricing formula is derived for defaultable bonds. On the basis of the above, an empirical study is made on the dynamics of the term structure of defaultable bonds in China in a three-factor defaultable HJM framework with stochastic volatility, using AAA corporate bond data, which demonstrates that there are significant correlations among the default-free short rate, the instantaneous short-term credit spread and the stochastic volatility. It is also found that the default-free short rate makes more contribution to the volatility of the defaultable short rate when the defaultable rate goes up, while the short-term credit spread makes more contribution when the defaultable rate goes down.The research is sponsored by National Natural Science Foundation of China (Grant No. 70771075) and Doctoral Fund of Ministry of Education of China (Grant No. 200800560032).