Estimation of term structure using Nelson-Siegel method

Abstract

The term structure of interest rates also called the yield curve refers to the relationship between the interest rates and term to maturity in an economy. In general, the interest rates increase with time as the risk associated with a long term investment is more. Hence the yield curve is likely to follow a trend given in the graph below. It is an important relationship because it is used to value all fixed income instruments. Any fixed income instrument can be modelled as a series of cash flows in the future which are discounted by the appropriate discount factors or yields. These yields are derived using the yield curve or the term structure of interest rates. In developed countries like the US and UK which have a well-developed bond market, several studies have been done to determine the term structure. On the other hand, in India which has a dormant bond market, these studies have been more recent. The term structure once derived has several applications such as to value government securities on days when it does not trade, creating a government bond index, pricing non-government fixed income instruments and corporate bonds, analyzing impact of monetary policy and so on. Hence, overall it is important to have an estimate of the term structure. The purpose of this paper is two-fold. First is to replicate the results of the term structure obtained by Gangadhar Darhba, Sudipata Dutta Roy and Vardhana Pawaskar. In the process this paper will aim to detail out the steps so as to make it easy to replicate by any finance enthusiast. The second purpose is to critique the paper and give some specific recommendations to improve the model.