Study On Term Structure Of Interest Rate Modelling And Application With Regime-Switching

Term structure of interest rate is one of the most active research fields on finance theory and application. It is the benchmark for asset pricing, financial product design, hedging, risk management, arbitrage and speculation. With the development of financial markets, the deepening of financial innovations and the market-oriented process of interest rate, the importance of term structure research is more and more obvious in China. The dissertation employs the theory and methods of financial mathematics to study theoretical basis of term structure of interest rates with regime-switching, static term structure of interest rates fitting model, term structure of interest rates dynamic model with regime - switching, empirical China's term structure of interest rates with regime-switching, bond option pricing with regime-switching. Combining the analysis of term structure of USA, the study shows that China's term structure of interest rates should be analyse with regime-switching. The results settle the theory foundation for modeling and application of term structure.Analyzing term structure of interest rate in theory, the dissertation establishes a theory framework of analysis on term structure of interest rate according yield rate, measures the level and volatility of yield curve, studies the factors of term structure of interest rate yield curve. After a characteristic analysis on regime-switching, the dissertation analizes judging criteria for regime-switching, reviews threshold model, mixture model, and Markov switching model on regime-switching.The dissertation analyzes the assumption of non-arbitrage, and defines discount function, spot rate and forward rate. Basing on the cubic B-spline function defined by difference quotient, the model designs the weights of treasury bonds, uses the variable roughness penalty method, and estimates parameters by second-difference operator. Selecting SEE T-bonds data for fitting, testing the model by accuracy and smoothness indices, the result shows that the model improves the calculating efficiency of fitting, performances good in accuracy and smoothness.The dissertation analyzes investment opportunity and objective function of consumer with regime-swithcing basing on the effection of state variables on the underlying economy. In the framework of CHLS interest rate model, the dissertation applies continuous two states Markov chain, develops a Hamilton interest rate model with regime-swithching, then extends the Markov regime-swithcing to three states specification, develops a three regime interest rate model without considering inflation. When regime-swithing probability is time-varying, the dissertation develops a dynamic interest rate model with combining interest rate movement with the past economy information, and estimates the parameters by Gibbs sampling.The dissertation makes a descriptive statistics and an unit root test on the monthly weighted average interest rate of CHIBOR, estimates the parameters of Hamilton term structure of interest rate with regime-switching, three states interest rate model and interest rate model with time-varying regime-swithing probability, then test the number of regmies, regime classification measure and forcast capability of three model. The results of the test show that the interest rate model with time-varying regime-swithing probability is suitable for descripting the interest rate of China.The dissertation analyzes the movement of interest, regime-switching and option pricing, prices the bond and bond option with regime-swithcing. Considering the regime-switching effects on interest rate derivatives pricing, the dissertation derives partial differential equation with Ito lemma, the characteristic function and recursion of bond option pricing, the relation between option value and initial regime probabilities, regime persistence, and estimated volatility.