THE FINANCIAL CALCULUS OF THE TERM STRUCTURE OF INTEREST RATE: ASYMPTOTIC COMPARISONS OF NELSON–SIEGEL AND DIEBOLD AND LI

Abstract

This paper explains the rationale behind the yield curve together with its applications and information content. It goes further to explain the spot and forward yield curves. This is achieved by developing the main theories which tend to describe the functional structure and behavior using continuity assumptions. We start with an introduction to the development of forward rate function using the Laplace transform and the yield curve specifically. The spot rate is then constructed to arrive at a non-linear polynomial whose coefficients can be estimated by ordinary Least Squares method and Nelson‐Siegel family techniques. The Nelson family technique is applied by financial institutions which have a lot of activities in financial markets.  Though it seems to be influential, It is not the only determinant of consumer prices in financial institutions and consequently it is advisable that market operators understand the functional behaviour of the curve and how to interpret it in analysis. An appraisal of yield curve is significant for both market players and financial institutions for efficient business decision. The curvature of yield function demonstrates the market expectation of future growth of financial market. The objective of this paper is to theoretically compare spot rates under the conditions of Diebold and Li with that of Nelson-Siegel in asymptotic values and derive an approximating curvature which possibly estimates spot rates when corresponding time varying parameters have been obtained. In this work we have used non-constraint optimization to estimate the parameteremploying time to maturities 24 months.