Modeling the term structure of interest rates in the Indian Debt market

Abstract

This paper explores the various techniques commonly used to estimate the term structure of interest rates from the prices of Government bonds, particularly bootstrapping, modeling the forward rate curve as an exponential function, the Bank of Canada ‘Super bell’ model and the Nelson-Siegel and Swenson approaches. We have also discussed the various methods of smoothing the interest rate curves thus obtained using splines. in a developing market like India, the number of liquid securities is quite small and they don’t cover all maturities. Hence illiquid securities, which trade at a liquidity premium, have to be incorporated into the time structure. The use of liquidity weighted objective functions for parameter estimation can be used to tackle this issue, where liquidity is modeled using observable quantities like the number and volume of trades in a security. The above models have been tested on data on the Indian Government, Bond market from Nov l, 2000 to Jan 15, 2001. We conclude that the Nelson- Siegel-Swenson method offers the best approach to pricing Goal bonds. g » Though we find an average error of about 10 paisa in the pricing of bonds as found by the methods (making the yield curves unsuitable for pricing with the bid ask spread being equal to 10 paisa) we have been able to observe the following phenomena. We have been able to prove statistically that the bonds trading below par are priced at a premium of more than 5 paisa over their economic value more than 98% of the time and more than '10 paisa for over 80% of the time. This we feel can be attributed to the practice in most treasuries of calculating the dealer profits as difference between sales and purchase prices (rather than mark to market) and bonds trading below par tend to approach the par value as they move towards maturity. Another reason could be that these bonds have a lower coupon and the ‘coupon effect’ could come into play. ' I We also found that the pricing error was minimum for bonds issued within the last 2 years and the 1 1.5% series of bonds for 2004. 2005, 2006, 2007, 2008, 2011 and 2015.