To Construct The Term Structure Curve Of Interest Rates Of National Debt Based On Index Spline Functions

The term structure curve of interest rates reflects the relationship of different maturity bonds and the corresponding interest rates.Reasonable term structure of interest rates is the basis of designing financial products and asset pricing.It has an important significance in the study of financial engineering.The study of the term structure of interest rates mainly has two phases.The initial study focused on qualitative description,and foreign scholars set up a quantitative model of term structure of interest rates after the 20th century 70s.Compared with foreign countries,China's bond market developed rapidly,but because of its late start,the market degree is not high,market structure does not balance,the bond variety is single and bond liquidity is poor,besides of that,the investor structure is unreasonable,there are still some deficiencies in China's bond market.Depth study of theory and model of term structure of interest rates,whether from the perspective of theory and practice,is of great significance.Term structure of interest rates is based on static estimates.The whole idea is based on current market prices of bonds traded,and fitting the data of bond markets with the application of a curve model,to estimate the bond market term structure of interest rates.Spline function is an important interest rate term structure model.Estimating the term structure of interest rates with the spline function greatly improved the accuracy of fitting.So far,the theory of fitting the term structure curve of interest rates based on the spline function is still not perfect enough.Scholars have done a large number of related exploration by using cubic-spline and B-spline theory.Yiyi Li proposed a node choosing option based on node deleting.Numerical experiments show that the fitting results is better than the traditional node choosing option.Qizhi He has done the empirical research on China's national debt data based on the exponential spline model.The research results show that the exponential spline model can reduce the bond pricing error.This paper borrows the idea of node choosing option based on node deleting,proposes a new algorithm based on exponential spline model.The algorithm is divided into four steps:1. Data selection:This paper selected 29 interest-bearing debt's closing price on Jan.8,2010 as the empirical research data.These 29 debts include short-,medium-and long-term debts.Their periods are between 3 to 20 years.In the empirical study,the data may make some limitations on the selection of the estimated term structure of interest rate.To avoid this limitation,the sample data will be divided into two groups,an experimental sample and a sample of testing. 2. Determine the value of parameterμ:In the exponential spline function,parameterμhas economic significance.This paper first estimate the value ofμ,and calculate the estimated values of other parameters,then do numerical experiments for differentμ.Finally we found that the fitting result was best whenμ=0.08.3. Select the number and location of the exponential spline function's node:First select the candidate node in the timeline.and establish exponential spline model.Then do the LSE to the exponential spline function.Use tha AIC criterion as the standard of selecting model.Finally,determined by calculating the node index for the spline model is (5-year,13-year,14-year).4. Comparison of the algorithm and the traditional model:Applicate this algorithm and the respective model to fit the data on the test samples,and construct China interest rate term structure curve.By comparing we found that this algorithm's fitting result is more better than the traditiona approach of cubic-spline model.There are three main improvements of the algorithm proposed in this paper.First,this paper use the exponential spline which has more better fitting results as the based model.Second, do numerical experiments for differentμaccording to bond trading data in China in recent years,then select the most suitable parameterμaccording to the experimental results.Third,this paper determine the number and location of the node by deleting the node point by point.