Construction of Nominal Yield Curve for Nairobi Securities Exchange: An Improvement on Monotone Preserving <i>r</i>(<i>t</i>)<i>t</i> Interpolation Method

Abstract

There is no agreed-upon method used to construct yield curves at the Nairobi Securities Exchange. The existing practice is that each financial company uses in-house methods to construct the yield curves for their pricing and decision making. The most common yield curve used in the market was the one constructed by the Cannon Asset Managers Limited (CAM), a Kenyan company, in 2011. The choice of the interpolation function is extremely important when constructing a yield curve. CAM used linear interpolation on the logarithms of the interest rates as their interpolation function. Studies have shown that all variations of linear interpolations produce discontinuities in the forward rate curve. The monotone convex interpolation method, introduced by Hagan & West [1], improved on the shortcomings of linear and cubic interpolations by ensuring not only a positive and (mostly) continuous forward rate curve, but also a strictly decreasing curve of discount factors. Unfortunately, the model not only depends heavily on an appropriate interpolation algorithm but also produces discontinuity of f ( t ) t under specific conditions. The monotone preserving r ( t ) t method improves on monotone convex method in that the knot points are estimated in the manner which ensures positivity and continuity in f ( t ) t besides preserving the geometry of r ( t ) t . Unfortunately, monotone preserving method has the undesirable characteristic of not being differentiable at the knot-points. This paper suggests an improvement on monotone preserving r ( t ) t interpolation method which ensures that the knot points of the curve are differentiable.