Constructing the Discount Function with Parsimonious Extended Nelson-Siegel Function: Evidence from Nigerian Eurobond

Abstract

Nigeria currently carrying out economic reforms is under the surveillance of institutional investors. To construct the market discount function through its yield curve, we applied the extended functional Nelson-Siegel parsimonious function with time-decay parameters to the Eurobond data to employ flexibility of the model and estimate the time varying parameters. In order to present a deep investigation of the Euro-bond market by reason of time to maturity, our contribution is anchored on following objectives: (i) construct the discount function (ii) investigate the limiting behavior of the yield curves and (iii) predict the in-sample yield. The data presented involves the daily closing of the Nigerian Eurobond yield covering January to December 2021 and 2022. The data was fitted to the observed Nigerian Eurobond yield curve to model the discount function. The ordinary least square method is used for the analysis and the estimated parameters were used to compute the in-sample yield. Test of goodness of fit was conducted showing that the model fits in well to the observed data demonstrated by the model’s R-square adjusted through the predicted yields after obtaining the two decay factors. This paper has implications on life insurance products associated with minimum guaranteed benefit schemes for the insured. Based on the terms and conditions of the contract, the insured pays regular premium invested in debt instruments and receives benefit at death or at maturity of the policy depending on the market performance of the fund. There is a guaranteed benefit which the insured earns irrespective of the performance of the life fund. The insurer would then pay the guaranteed amount even if the benefit eventually drops below the guaranteed amount. Given the discount 𝛿(𝜏)and benefit∅, the present value of future death benefits is modeled as 𝑃𝑉𝐹𝐵 = ∅1𝛿(1) + ∅2𝛿(2) + ⋯ + ∅𝑇−1𝛿(𝑇 − 1) + ∅𝑇𝛿(𝑇).