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.
Highlights
This was driven by the requirement of International Accounting Standard (IAS) 39, which requires that there should be a standard yield curve to facilitate investors in fixed income instruments to value their portfolios at fair market values
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 ) besides preserving the geometry of r (t )t
Monotone preserving method has the undesirable characteristic of not being differentiable at the knot-points
Summary
The Nairobi Securities Exchange (NSE) started trading in shares while Kenya was still a British colony in the 1920s, according to IFC/CBK [2]. In June 2010 Budget speech, the government of Kenya, through a policy pronouncement by the Deputy Prime Minister and Minister of Finance, announced that steps would be made towards developing institutional and legal frameworks to introduce a Commodities and Futures exchange in Kenya This will create a need to design a tool that can be used by the market to price the derivatives properly. According to Ngugi et al [8], leading stockbrokers, a group of bank traders and institutional fund managers were working with Reuters Limited in 2006 towards developing an acceptable, credible market yield curve This was driven by the requirement of International Accounting Standard (IAS) 39, which requires that there should be a standard yield curve to facilitate investors in fixed income instruments to value their portfolios at fair market values. We intend to use an interpolation method which has been verified as being superior to the variations of linear interpolation methods, and that is an improvement of monotone preserving r (t )t method
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