Forward Yield Curve Research Articles

Zero-Coupon, Forward, and Par Yield Curves for the Nigerian Bond Market

The Nigerian bond market is currently one of the most liquid in sub-Saharan Africa. Many African countries regard it as a model from which to learn and based on which to develop their respective bond markets. The developments achieved in the Nigerian bond market are of particular interest to both investors and fixed income analysts—both domestic and international. One of the important tools required for fixed income analysis, pricing, and trading is the yield curve. To the best of our knowledge, even though the Nigerian bond market has a secondary market yield curve, the yield curve is a yield-to-maturity curve, and not zero-coupon yield curve. The purpose of this study is to model the zero-coupon, par, and forward yield curves for the Nigerian bond market. We use various methods such as the piecewise cubic Hermite method, the piecewise cubic spline method (with not-a-knot end condition), the Nelson–Siegel–Svensson method, and the variable roughness penalty method. Data are obtained from the FMDQ OTC website. The results show that the piecewise cubic Hermite method is very suitable for producing the Nigerian par and zero-coupon yield curves. Our best recommended method for producing the Nigerian zero-coupon yield curve is therefore the piecewise cubic Hermite method, followed by the Nelson–Siegel–Svensson method. For the forward yield curve, the results show that the best method is the Nelson–Siegel–Svensson method, followed by the variable roughness penalty method.

Zero-Coupon and Forward Yield Curves for Government of Ghana Bonds

This article seeks to provide a framework for modeling daily zero-coupon yield curve for Government of Ghana bonds based on secondary market daily trades. It also proposes method for modeling the forward yield curve. The current practice in Ghana is to produce yield curve for Government of Ghana bonds based on primary market weekly auctions. This article demonstrates the extraction and fitting of secondary market daily yield curves for Government of Ghana bonds, using bootstrapping and piecewise cubic hermite interpolation. The article also compares the piecewise cubic hermite method with the piecewise cubic spline method, the Nelson–Siegel–Svensson model, and the penalized smoothing spline method. Data used are the daily bond price data from the Ghana Fixed Income Market, accessible at the Central Securities Depository of Ghana. The results show yield curves that reflect the actual daily yield movements in the secondary bond market of Ghana. The results also show that the piecewise cubic hermite method fits the zero-coupon yield curve better than the other methods as far as the Ghanaian bond market is concerned. For the forward curves, we recommend that either or both of the piecewise cubic hermite method and the Nelson–Siegel–Svensson method could be used by the market participants.

Macroeconomic shocks and the forward yield curve: how important is monetary policy?

The associations between macroeconomic fluctuations and the yield curve tend to be explained by the reactions of the monetary authority. This paper evaluates how macroeconomics shocks affect the forward yield curve for domestic and foreign debt markets in Venezuela, where monetary policy is not the main source of macroeconomic fluctuations. As previous results in the literature, macroeconomic shocks affect more strongly the short end of the yield curve in the expected direction. Overall, supply shocks explain most of the variability of long-term yields, spread and volatility. Nonetheless, short-term yield movements can be associated with general monetary conditions of the economy and not necessarily with monetary policy actions.

Forward Curve Shifts and Return Convergence

Most investment-grade bond portfolios have a relatively stable duration that shapes their multiyear returns. These returns are impacted by the wide variety of yield paths that can result from sequential migrations to implied forward yield curves, accompanied by parallel trend line shifts. Under these theoretical conditions, the annualized return converges, over an investment horizon that is roughly twice the portfolio’s duration, toward a starting yield curve value whose maturity just coincides with this specific horizon. Thus, a stable duration portfolio return will converge, with surprisingly minimal dispersions, back to a yield curve value that prevailed at the outset—regardless of the direction or volatility of intervening yields. These results have important implications for multiyear return estimation and for volatility assumptions involved in asset allocation. <b>TOPICS:</b>Portfolio management/multi-asset allocation, in portfolio management, commodities

Direct Extracting the Implied Forward Yield Curve from the Coupon Bond Prices

It is developed the analytical approach based on the future value concept to directly extract the forward yield curve from the fixed coupon-bearing bond prices. It meets the next no-arbitrage condition: the rates of return on zero-coupon and coupon bonds with the same maturities should be equal. It is shown that there are the essential differences between the estimates of yield curves obtained by the direct and indirect methods. It is suggested to employ only direct methods to extract the spot and forward yield curves: the spot yield curve is directly extracted using the present value concept, and at the same time the forward yield curve is directly extracted using the future value one. It is shown that there is a complementary set of forward rates meeting the no-arbitrage condition side by side with a set of forward rates defined by standard approach.

Frontiers in financial dynamics

In recent decades, mathematical motivated financial models have been used to understand the complexity and intermittent nature of financial market instruments. Typically, applied mathematics models a physical system by specifying and quantifying the physical laws to which the process should theoretically conform. Such theoretical models are often represented as differential equations. The solutions of these differential equations have been shown to have poor compliance with observed financial data which has been attributed to difficulties in correctly estimating the parameters of the differential equation. Generalised smoothing provides a comprehensive evaluation of financial dynamics as it accurately estimates data driven parameters for differential equations and produces a fitted curve that incorporates the theoretical specifications implied by the differential equation while adhering to the observed financial data. This article demonstrates the merit for a generalised smoothing approach to modeling financial dynamics by examining instantaneous forward yield curves within a generalised smoothing framework.

Disinflationary Monetary Strategy and Instability of the Forward Yield Curve: The Case of the Czech Republic, 1999–2005

In this study I describe the relationship between monetary policy and medium and long-term swap rates. I focus especially on explanation of the instability of the level and relations of swap and forward rates on the Czech swap market in the context of the Czech National Bank's (CNB) disinflation policy based on direct inflation targeting. Theoretically the main source of this problem is the inconsistency between the central bank's current and expected policy and the anticipated course of economic fundamentals. A common feature is that during disinflation the level of monetary policy restriction is not stable over time and is hard to predict for investors. Besides objective factors such as fluctuating economic growth or limited scope of information, this is also a result of the instability of sensitivity parameters of the central bank's reaction function and of the character of the monetary strategy pursued. Empirical analysis showed a limited effect of changes in the CNB repo rate on the instantaneous adaptation of swap and forward rates. In addition, problems connected with the CNB's weakened credibility were immediately identified, along with related erroneous expectations of investors. I interpret the instability of relations as evidence of differences in investors' inflation predictions of a gradual tendency for the economy to reach a state of low inflation.

Fitting term structure of interest rates using B-splines: the case of Taiwanese Government bonds

The B-spline curve fitting technique is one of the most popular empirical methodologies for estimating the term structure of interest rates, due to its stability and reliability in practical applications. This paper applies the B-spline technique to estimating the term structure for an important small-sized emerging bond market, the Taiwanese Government Bond (TGB) market. Regardless of the efficiency of the obsrved market data, several issues are investigated when applying this fitting technique. The application of the B-spline functions is first discussed to approximate the discount function, spot yield curve and forward yield curve respectively. The coupon payment effect on the TGB price is identified and is incorporated into the model estimation. A sensitivity analysis for the B-spline technique is performed with respect to changes in the within-sample knots, and a feasible method suggested for choosing the optimal knots within the approximation space in view of standard pricing error minimization. The results show that the B-spline methodology, when applied to discount fitting and spot fitting, is satisfactory in obtaining reliable term structure. It is also not very sensitive to some ad hoc choices in the model estimation.

Fitting the term structure of interest rates for Taiwanese government bonds

The term structure of interest rates provides a basis for pricing fixed-income securities and interest rate derivative securities as well as other capital assets. Unfortunately, the term structure is not always directly observable because most of the substitutes for default-free bonds are not pure discount bonds. We use curve fitting techniques with the observed government coupon bond prices to estimate the term structure. In this paper, the B-spline approximation is used to estimate the Taiwanese Government Bond (TGB) term structure. We apply the B-spline functions to approximate the discount function, spot yield curve, and forward yield curve respectively. Among the three approaches, the discount fitting approach and the spot fitting approach are reasonable and reliable, but the spot fitting approach achieves the most suitable fit. Using this methodology, we can investigate term structure fitting problems, identify coupon effects, and analyze factors which drive term structure fluctuations in the TGB market.

Yield Curve Modelling at the Bank of Canada

The primary objective of this paper is to produce a framework that could be used to construct a historical data base of zero-coupon and forward yield curves estimated from Government of Canada securities' prices.