Research On Static Fitting Models And Application Of Interest Rate Term Structure

Fitting the term structure of interest rates is a very important subject offinancial mathematics. The research on interest rate term structure has majortheoretical and practical significance on the asset pricing, design of financialgoods and risk management. In this paper, the modeling principle andapplicability of static models and dynamic models of interest rate termstructure are analysed in detail. And according to the static fitting models, thepenalized splines model and the Nelson-Siegel expanded models of interestrate term structure are studied, and parameters estimation procedures aregiven. Finally, the research results are applied in the fitting credit spreads. Themain contents and innovations of the paper are as follows.1For the problem of overfitting the curve, the penalized splines modelof interest rate term structure is developed to estimate the term structure. Afterselecting spline knots by stepwise deletion method, the generalizedcross-validation method is used to choose the penalty factor, and geneticalgorithm is applied to look for the optimal penalty factor. The empiricalresults show that the penalized splines model can improve the curve fitting smoothness but possibly decrease the curve fitting accuracy.2NS model, SV model, NSM model, FF model and SF model of theNelson-Siegel class of interest rate term structure are summarized in theory,and parameters estimation procedures based on genetic algorithm are given.Finally, the trading data of government bonds in Shanghai Stock Exchange areapplied to compare the five models mentioned above. The empirical resultsshow that the fitting accuracy and flexibility of FF model and SF model aresuperior to the other Nelson-Siegel class models, and they are suitable forChina's bond market.3Static fitting models of interest rate term structure are applied to buildthe credit spreads fitting model and joint-estimate the credit spreads withJarrow reduced form model. This method is based on the market prices ofcorporate bonds, and suits for the actually observed credit spreads.