Research On The Term Structure Of National Debt Interest Rates Based On The Dynamic Nelson-Siegel Model

Treasury bond yield is the benchmark interest rate for the operation of economic and financial markets and the yield curve is a basic tool to analyze the trend of interest rate and market pricing.However,the spot interest rate in the yield curve can only be obtained by analyzing the market data.Therefore,in the study of interest rate term structure model,by establishing a stable mathematical model and accurately calculating the spot interest rate and the yield curve,we can study the crosssection characteristics and time series characteristics of the yield curve.At the meantime,it can be applied into the pricing and risk management of interest rate derivatives in other studies.The study of the cross-section characteristics of the yield curve means that a small number of representative factors are used to explain the yield of different periods in a specific time section.The research on the characteristics of time series is also called dynamic research,which needs to meet the needs of continuous change of a single time section and to obtain dynamic characteristics for practical application.Domestic and foreign academic research on the term structure of national treasury interest rate and its practical application have developed rapidly in the past decades.This paper selected dynamic Nelson-Siegel model(DNS)and non-arbitrage dynamic Nelson-Siegel model(AFNS)as two benchmark model to construct the Chinese Treasury bond yield curve and to analyze the market characteristics.With the wide application of DNS model,this paper innovated that the transfer matrix of the state equation of the DNS model will be divided into diagonal and off-diagonal forms,which equals to apply zero constraint to the partial element in the matrix,constructing the full parameters and non-full parameters DNS models.By fitting the data of the Chinese Treasury yields respectively we can find out whether zero constraint has its necessity and whether the DNS model can be easily operated in the estimation process.Next this paper discussed whether no arbitrage restrictions in Chinese treasury bond market has its necessity.The slight advantage of non-arbitrage dynamic Nelson-Siegel model(AFNS)in the empirical results turns out that the no arbitrage restrictions in Chinese treasury bond market must exist.At the same time,this paper made an empirical analysis on the three NS models to compare the fitting effect and prediction performance of these three models to find out which is better.The conclusion further illustrates that both DNS model and AFNS model are suitable for the interest rate term structure model of Chinese Treasury bond market and can also be used for more analysis in the future research.For DNS model,the all-parameter model is better in terms of interpretation ability and model performance than the non-full parameter model and also has better prediction effect.Therefore,it can be concluded that partial zero constraint of transfer matrix will limit the interpretation ability of DNS model so the full parameters are necessary.However,for the sake of simple operation or any other appropriate situation,it will also be a good choice to use the non-full parameter model to estimate.Meanwhile in the comprehensive comparison,the in-sample fitting ability of AFNS model is higher than that of the original DNS model and also AFNS model has a better performance in prediction.Therefore,the non-arbitrage factor should be considered in studying the term structure of Treasury interest rate.At the same time,when DNS model and AFNS model are estimated under comprehensive comparison,it is actually a test of whether the market can meet the arbitrage free nature.This paper also indirectly proves that China's bond market is not completely arbitrage free.