We seek to determine which yield curve construction method produces the best zero coupon yield curve (ZCYC) for Nairobi Securities Exchange (NSE). The ZCYC should be differentiable at all points and at the same time, should produce a continuous and positive forward curve at all knot points. A decreasing discount curve is also expected from the resulting ZCYC, as an indication of monotonicity. For the interpolation method, we will use an improvement of monotone preserving interpolation method on r(t)t, while the Nelson and Siegel [1] model is the parametric model of choice. This is because compared to other interpolation methods, the improvement of monotone preserving interpolation method on  r(t)t produces curves with the desirable trait of differentiability, while the Nelson-Siegel [1] model is shown to produce the best-fit results for Kenyan bond data. We compare the models’ performance in terms of accuracy in pricing back the fixed-income securities. For this study, we use bond data from Central Bank of Kenya (CBK). The better of the two methods will be used for the Kenyan securities market and, consequently, the East African Securities markets.