The Research Of Estimating The Term Structure With Spline Function Based On M-SCAD Criterion

Term structure of interest rate has been an important issue in the financial world because it evaluates the relationship between yield to maturity and term under same risk exposure at some point. The reform of interest rate in China requires us to emphasize more on term structure of interest rate analysis. For the same reason, we need to construct a reliable, stable and complete term structure of interest curve.In the first part, we first review some fundamental theories in the bond market which include bond pricing formula and some basic knowledge of term structure of interest rate. After that, we compare and summarize the fitting methods of static term structure of interest rate which include polynomial spline method, exponential spline function method, exponential curve function method, B-splines method and smooth spline function method.The second part is the focus of this article and it mainly discusses how to construct term structure and parameter estimation. Although a series of empirical researches on term structure of interest have been done, but we still need to continue to improve its research. In chapter3, after considering quantile regression and LAD-LASSO, we introduce penalized quantile regression to term structure from Wu(2009) because it is much stable. The advantage of this model is that it can do parameter estimation and the knot selection at the same time. Besides, it also retains some strong points of LAD-LASSO and it is a special case of quantile regression. In chapter4, based on the smoothing clipped absolute deviation model which from Fan(2001), we apply M estimation from Huber(1981) to construct a term structure model. This model expands LAD-LASSO and also enables us to do knot selection and parameter estimation at the same time. When we use this method to construct the term structure of treasure bills in SSE (Shanghai Stock Exchange), reveal that the model has a better robustness. In addition, the out-of-sample forecasting results show that the model can improve the pricing precision of bonds compared to traditional methods.Lastly, we sum up the main topics in this article and put forward some further questions.