A Study On Term Structure Of Interest Rate Based On Dynamic NS-DE Model

As the key of financial product pricing, Term Structure of Interest Rates always isthe research hotspot. In the past30years, the theory and practice have developed a lot,the field of study include the pricing of derivatives, portfolio, simulate and forecastinterest. Economist hope to forecast the trends of interest fluctuation, and investor wantto find a useful interest curve to make invest decision. So, many financial institutionsdevote to develop and improve related models. The thesis research the Term Structure ofChinese bonds interest using Nelson and Siegel model.Before the research, we have to disposal data of the bonds. First, the bonds tradedin more than one market and the illiquid. The OTC facing retail investor and we couldnot use these data as the light volume. The inter-bank market also could not as theilliquid. So the only choice is the exchange bonds data. Second, the Term Structure areincomplete, most of them are midterm and long term bond and lack of short term bondespecially less than1year. Using these data for Nelson-Siegel model was inadequacybecause the NS model was sensitively for short term bond. At last, we use inter-bankPledge-style Repo interest rate to replace the short term rate.In the empirical study, we firstly construct Term Structure model by State-spacemodel, and define the three parameter as the state variable in State-space model anddefine them submit to VAR possess. Then use the Kalman Filter for solution. For thetime varying variable λ, we solve it by Maximum Likelihood Estimation. So we couldget the Term Structure of Interest Rates in the sample size and forecast. Secondly, westatic fitting the Term Structure using the λ we got by Kalman Filter and using threeoptimization algorithm which is Nonlinear Least Square Method, Genetic Algorithmand Differential Evolution. The GA and DE is global optimality algorithm, but themutation and select process in both algorithms are totally different. DE is better inself-adaption and more accurate and robustness than any other Evolution Algorithms. Inthe paper, we compare the result of the DE Algorithm and NLLS, GA, the result showus that the RMSE of the Term Structure by DE Algorithm is much low than otheralgorithms and we show it by4graphs. Thirdly, we forecast the Term Structure usingthe result of the DE Algorithm by AR, VAR and VAR-Macro process. The conclusion ismodeling the dynamic Term Structure of Interest Rates model should constructState-space model to solve the time-varying variable and using it in static fitting, and then optimum by DE Algorithm, at last forecast using AR for short term and VAR forLong term.The innovation points in this paper: estimating the parameters using DE Algorithmand compare to NLLS and GA; Constructing NS model by State-space form and solveand forecast by Kalman Filter; Add macro factors in VAR model and observe whether itwill enhance the forecast.