The optimization of continuous discount function through the continuous yield curve trajectories involving the parsimonious Nelson-siegel model

Abstract

Yield curves which explain the variation in interest rates over varying maturities, provide important indicators with potentially useful implications on the investment choices, risk management strategies of financial institutions and fiscal policies of regulators. Accurately estimating the parsimonious parameters of the yield curve and modelling the discount function is highly important. The continuous forward rate function is a transformed discount function as a numerical device employed to obtain the price of a collection of bonds since the present value of a set of cash flows is computed by finding the product of these cash flows and the associated discount function. Nigeria’s bond market representing a major segment of the capital market and an important means of monetary transmission framework has suffered continuous liquidity problems. The lack of functional capital market instruments in form of government bonds has accounted for the poor performance of bond market. Consequently, this study intends to (i) Compute the discount function and (ii) Show its applications on life insurance offerings. This study analysed the term structure of interest rates using the Nigerian Eurobond which was collected for the years 2018 and 2019 from which the discount functions were constructed by adopting the continuous Nelson Siegel continuous function. A t-test conducted on the adjusted R2 on the model using Ordinary Least Square method after fixing the shape parameters was applied after computing the exponentially decaying factor. Computational evidence from the results reveals that the adjusted 𝑅square for 2018 and 2019 are 0.976and respectively0.986. This indicates that 97.6%of 2018 and 98.6% of the observed data can be explained by the Nelson-Siegel model of data using the estimated parameters for the two years and hence the result suggests a high level of accuracy confirming the degree to which the Nelson-Siegel yield curve parameters has estimated the illiquid Nigerian financial market.