We seek to construct a zero coupon yield curve (ZCYC) for Nairobi Securities Exchange (NSE). The objective of this paper is to construct a ZCYC that is differentiable at all points and at the same time, produces continuous and positive forward curve. We will use the classical Nelson-Siegel model, Svensson Model, Rezende-Ferreira model and Svensson extended model. These models have linear and nonlinear guidelines making them have multiple local minima. This condition causes model estimation more difficult to estimate. We therefore use L-BFGS-B method as the optimization approach for estimating the models. We compare the models’ performance in terms of continuity and differentiability of the ZCYC, and positivity of the forward curve. We use bond data from Central Bank of Kenya (CBK). The best parametric model to be used for the Kenyan securities market and, consequently, the East African Securities markets is chosen if and only if it depicts the aforementioned qualities.