Zero-coupon Yield Curve Research Articles

Construction of Zero-Coupon Yield Curve From Coupon Bond Yield Using Australian Data

This paper briefly surveys the various approaches to modelling the zero coupon yield curve is the starting point for much finance research. The method adopted here for the Australian Treasury bond data is based upon polynomial spline fitting, but with the constraint that the long end of the term structure is stable. This approach has also been successfully applied to the Danish bond market (Tanggaard and Jakobsen (1988)). The forward rate curve then becomes the important input data for the modelling of the term structure of interest rates and pricing of interest rate contingent claims using the Heath-Jarrow-Morton (1992) model.

Nonparametric Estimation of a Multifactor Heath-Jarrow-Morton Model: An Integrated Approach

We propose a new nonparametric estimator for the volatility structure of the zero-coupon yield curve inside the Heath-Jarrow-Morton framework. The estimator incorporates cross-sectional restrictions along the maturity dimension, and also allows for measurement errors, which can arise from estimation of the yield curve from noisy data. The estimates are implemented with daily CRSP bond data.

Value at Risk: Concept and It's Implementation for Indian Banking System

Value-at-Risk (VaR) has been widely promoted by the Bank for International Settlement (BIS) as well as central banks of all countries as a way of monitoring and managing market risk and as a basis for setting regulatory minimum capital standards. The revised Basle Accord, implemented in January 1998, makes it mandatory for banks to use VaR as a basis for determining the amount of regulatory capital adequate for covering market risk. For market participants like Banks and Primary Dealers (PDs) in the Indian financial sector, it has become imperative to use VaR methods to calculate the regulatory capital charge required. The RBI has issued guidelines for PDs. We have adopted three categories of VaR methods, viz., Variance-Covariance (Normal) methods including Risk-Metric, Historical Simulation (HS) and Tail-Index Based approach. The Zero-Coupon Yield Curve (ZCYC) compiled by National Stock Exchange (NSE) has been used to price the bonds as well as portfolios. Estimated VaRs are validated by carrying out back testing based on last one year's data. Empirical results show that normal methods, in particularly the Risk-Metric approach, underestimate VaR numbers substantially resulting to too many failures in backtesting. Historical simulation provides more accurate VaR estimates, and indicates capital charge higher than those obtained through normal methods. The tail-index (Hill's estimator) based method also perform quite well though at times it provides too conservative VaR estimates - higher than all other competing VaR models considered here and occasions of VaR violation in backtesting are less than expected number for each bond/portfolio.

Using Treasury STRIPS to Measure the Yield Curve

Treasury STRIPS derived from coupon payments of notes and bonds provide an effective reading of the zero-coupon yield curve. Among their advantages, coupon STRIPS are zero-coupon securities, have a complete range of maturities, and are fungible, which appears to make the coupon STRIPS yield curve relatively smooth. Yields on coupon STRIPS are compared to the zero-coupon yield curves derived from notes and bonds under the Nelson-Siegel and the Fisher-Nychka-Zervos methods. The results point to some shortcomings of these approaches and indicate that the zero-coupon yield curve could be estimated more precisely from coupon STRIPS.

Using Treasury STRIPS to Measure the Yield Curve

Treasury STRIPS derived from coupon payments of notes and bonds provide an effective reading of the zero-coupon yield curve. Among their advantages, coupon STRIPS are zero-coupon securities, have a complete range of maturities, and are fungible, which appears to make the coupon STRIPS yield curve relatively smooth. Yields on coupon STRIPS are compared to the zero-coupon yield curves derived from notes and bonds under the Nelson-Siegel and the Fisher-Nychka-Zervos methods. The results point to some shortcomings of these approaches and indicate that the zero-coupon yield curve could be estimated more precisely from coupon STRIPS.

Estimation of the term structure of interest rates: an international perspective

The overall objective of this paper is to introduce a new methodology of fitting the term structure of interest rates or zero-coupon yield curves. Toward this end, Chebyshev polynomials are incorporated into a quantity called the interest cumulator and then subjected to a minimization procedure to yield parameters that subsequently maps out zero-coupon yield curves. This methodology is applied to Australian coupon bond data to estimate such yield curves. An international perspective is then provided by a comparison and contrast with international evidence in this area. Several innovations of the paper are discerned: (i) while Chebyshev polynomials are well known in engineering and science, this paper is the first to use it to develop a method to fit zero-coupon yield curves from observed coupon paying bond prices; (ii) the estimation procedure based upon the logarithm norm is found to be superior to the standard form based upon the price norm; (iii) Chebyshev polynomials possess desirable properties that improve the econometrics of yield curve fitting; (iv) the empirical results reveal exceptional goodness of fit; and (v) these results are the first published Australian zero-coupon yield curves.

The Information Content of the Term Structure: An Application to French Government Bonds (in French)

This paper evaluates the information content of the term structure about future changes in interest rates and changes in inflation rate, in France. A data set has been constructed, which contains zero-coupon yield curves on government bonds over the period 1980-95. The information content is generally very weak over the whole period. On the contrary, over the period 1985-95, the term structure contains information for certain maturities. On the one hand, spreads vis-a-vis 2-year rates are informative for future changes in short-term rates, whereas spreads vis-a-vis 3-year rates are informative for both future changes in short-term rates and future changes in long-term rates; on the second hand, the spreads from (2- versus 1-year rates) to (5- versus 1-year rates) and (4- versus 2-year rates) are the most informative for future changes in inflation rate.

Comparison of Tax Rates Inferred from Zero-Coupon Yield Curves

Comparison of Tax Rates Inferred from Zero-Coupon Yield Curves

Interest rate volatility and the shape of the term structure

This paper analyses the effect of interest rate uncertainty on the shape of the forward rate curve. We consider a broad class of term structure models characterized by an affine relation between the drift and diffusion coefficients of the stochastic process describing the evolution of the state variables and the level of the state variables. For these models, a simple relation exists between the shape of the forward rate curve, the sensitivity of the zero-coupon yield curve to the state variables and the variance-covariance matrix of the state variables. In single factor models this relation implies that minus the convexity of the forward rate curve with respect to a measure of ‘duration’ is equal to the variance of the short rate. The paper explores why it is that, despite the well known shortcomings of single factor models, attempts to fit such models to cross-sections of nominal bond prices nonetheless produce reasonable estimates of interest rate volatility.