Yield curve estimation of the Nelson-Siegel class model by using hybrid method with L-BFGS-B iterations approach

Abstract

This paper discussed about model extension in determines the yield curve. Determine of yield curve using Nelson-Siegel class model. This class model consisting of: 3-factor model, 4-factor model, the 5-factor model, and 6-factor model. 6-factor model is a model extended from 5-factor models. The extension aims to increase the level of accuracy in determine the yield curve. Nelson-Siegel class model is model that more difficult to estimate because it has two shape the parameters, i.e. the linear and nonlinear parameters. Extension of this model is done by adding the fourth hump into 5-factor model. In addition, we obtain new model, this model have local minimum multiple so that it is more difficult to be estimated. To estimate this model, we propose estimation using a hybrid method. Hybrid method is combines method of estimation the nonlinear least squares with constrained optimization, and then continued with L-BFGS-B iteration approach. Estimation of the class model was done by full estimation, i.e. estimating the linear parameters and nonlinear parameters simultaneously. Then, we calculated MSE, AIC, and BIC. The purpose of calculating this component is to determine the best of model. The best model obtainable if the models have component value which is smaller than the other models. This paper uses data from Indonesian government bonds. Based on data processing, we obtained the best model i.e. 6- factors model.