Zero-Coupon, Forward, and Par Yield Curves for the Nigerian Bond Market

The Nigerian bond market is currently one of the most liquid in sub-Saharan Africa. Many African countries regard it as a model from which to learn and based on which to develop their respective bond markets. The developments achieved in the Nigerian bond market are of particular interest to both investors and fixed income analysts—both domestic and international. One of the important tools required for fixed income analysis, pricing, and trading is the yield curve. To the best of our knowledge, even though the Nigerian bond market has a secondary market yield curve, the yield curve is a yield-to-maturity curve, and not zero-coupon yield curve. The purpose of this study is to model the zero-coupon, par, and forward yield curves for the Nigerian bond market. We use various methods such as the piecewise cubic Hermite method, the piecewise cubic spline method (with not-a-knot end condition), the Nelson–Siegel–Svensson method, and the variable roughness penalty method. Data are obtained from the FMDQ OTC website. The results show that the piecewise cubic Hermite method is very suitable for producing the Nigerian par and zero-coupon yield curves. Our best recommended method for producing the Nigerian zero-coupon yield curve is therefore the piecewise cubic Hermite method, followed by the Nelson–Siegel–Svensson method. For the forward yield curve, the results show that the best method is the Nelson–Siegel–Svensson method, followed by the variable roughness penalty method.

Smoothing Wind and Rainfall Data through Functional Data Analysis Technique

The pattern of wind and rainfall throughout Peninsular Malaysia are varied from one region to another, because of strong influences from the monsoons. In order to capture the wind and rainfall variations, a functional data analysis is introduced. The purpose of this study is to convert the wind and rainfall data into a smooth curve by using functional data analysis method. Fourier basis is used in this study since the wind and rainfall data indicated periodic pattern. In order to avoid such overfitting data, roughness penalty is added to the least square when constructing functional data object from the observed data. Result indicated that if we use a small number of bases functions, the difference is very small between with and without roughness penalty, showing that it is safer to smooth only when required. However, when a large basis function is employed, the roughness penalty should be added in order to obtain optimal fit data. Based on the contour plot of correlation and cross-correlation functions of wind and rainfall data, the relationship between both climate functions could be determined.