Research On The Improvement Of Cubic Spline Function

This paper research how to estibalish term structure of interest. It compares various models.We get a new spline function by combined with the cubic spline function method and the interpolation cubic spline function.A yield curve that is built by new function more fully reflect the market information, more fully explor e the connotation of the sample.This paper first introduces the research background, purpose and significance of the study.China’s bond market matures, the price discovery function gradually increased, the bond market can provide the information required by the term structure of interest rates. In order to provide a variety of financial products pricing benchmark, in order to provide the required information of interest rate risk management and improve the purchase of debt yield curve, thus improving the fitting model of the term structure of interest rates. This is related to pricing and management with help. Then reviews the term structure of interest rate in economic theory, and made a comparison. This paper compares the fitting model of the term structure of interest rates. Describes the advantages and disadvantages of each model and the existing research results. The object of the bond transaction data generated involved is introduced, including the issuance of government bonds in history, the Shanghai stock exchange, the inter-bank bond market. And pointed out that due to the inter-bank bond market position in the bond market, the transaction data is selected as the empirical data used. After given the cubic spline function method the concrete method of improving will set the discount factor of the cubic spline function transformation, all the parameters of the original method are through the parameter estimation has linear regression, the improved method which will be a parameter with a zero coupon bond interest rate term related information to solve, and the rest through linear regression obtained. The estimated total process to do a detailed demonstration from the pricing formula parameters of three spline function method and the improved three spline function method. An empirical research is carried out in the fourth chapter. Choose the trading day and the trading days more than bond empirical, benefits the improvement were compared before and after the construction of the rate difference between two curves, on the improved effect is not ideal trading day, through the analysis of choice maturity close to zero bond as directly reflects the interest rate term structure of bonds, it is found that compared with the original method, the overall fitting error is reduced or similar, according to the income rate curve calculated bond theory price and the actual transaction price is close to the construction of good results.In this paper, from the empirical results show that the new treasury yield rate curve can be directly through the known rate of return and the corresponding time points, and by selecting more than bonds after several rounds of screening can make new revenue rate fitting error is reduced or not significantly increased at the same time, the curve shape is reasonable.