Natural Cubic Splines Yield Curve

Fitting of smooth yield curve

The fitting of smooth curve through a set of data points and extention to this is the fitting of 'best fit' spline to a large set of data points which show the cerrent trend but which do not all lie above the curve. The method involves cluster analysis, that is, grouping the crude data into clusters and seed points are the limites of each cluster. The central for each clustrer become nodes through which a natural spline is fitted. There are five stages nessesary in the cluster analysis and calculation of node positions, summerised as follow: 1. starting with choosing seed points 2. determine two data point which are closest to each seed point (the nearest neighbour pair) 3. calculate the coordinate of weighted average of each nearest neighbour pair. 4. allocate the remaining data points to their appropriate cluster. 5. calculate the cordinate of the central point of each cluster, using weight average. This method can be used for approximation yield curve (with gross yields or zero yields), which is shown in those matlab code.