The Term Structure Of Interest Rate Static Modeling And Estimation

The term structure of interest rates refers to the relationship between spot rates of zero-coupon securities and their terms of maturity. The plot of interest rates of bonds against their terms is called the"yield curve". Economists and investors believe that the shape of the yield curve reflects the market's future expectation of interest rates and the associated monetary policy. Therefore, the term structure of interest rates is one of the most important economic variables. With the advance of the interest rate marketization in China, the demand and supply of capitals in financial market is becoming the most important factor in the interest rate variation. As the interest rate changes more frequently, modeling the term structure of interest rates and constructing a yield curve become more important.This thesis discusses some theoretical and empirical topics on interest rate modeling and estimation. In the second chapter, four main hypotheses on the formulation of term structure are reviewed: expectation hypothesis, market segmentation hypothesis, liquidity preference hypothesis, and preferred habitat hypothesis. The third chapter summarizes the development of Chinese interest rate market. We introduce the main benchmark interest rates, including London Interbank Offered Rate (LIBOR) and the federal funds rate. The literature review of the static approximation of interest rate term structure is presented in the fourth chapter. Classical and modern estimation methods of the static model of interest rate term structure are also reviewed: McCulloch's Cubit Spline Function, Vasicek and Gong's exponential spline method, Steeley's B-spline method, Fisher and Nychka's smoothing spline method, and Nelson-Siegel model.The second part of this thesis, which consists of Chapter 5 to 8, focuses on modeling interest rates, applying statistical approaches to estimate model parameters, and generating a complete fit of the yield curve for prediction.In the fifth chapter, we propose to estimate the number and position of knots to improve the cubic spline model. Instead of using the least squares (LS) estimation in the traditional model, we develope a least absolute deviations (LAD) approach for estimating the parameters of cubic spline function in Chapter 6. In chapter 7,we propose a novel modeling approach by combining LAD and variable selection, which uses hypothesis testing and the BIC criterion for variable selection. Furthermore, we apply LAD-LASSO to perform variable selection and parameter estimation simultaneously in Chapter 8. The propose methods are used to estimate the Shanghai stock exchange term structure of interest rates with cubic spline function. The forecasting power of the new method is compared with the method of traditional knot settings in the literature.Finally, the main contents and conclusions of this dissertation are summarized, and future research directions are also discussed.