Zero-coupon yield curve estimation from a central bank perspective

Since in recent years a relatively liquid and transparent market of government securities has emerged in Hungary, it seems straightforward for the monetary authority to try to extract information about market expectations of future nominal interest rates and inflation from the prices of these assets. However, drawing a conclusion from the prices of T-bills and -bonds concerning either nominal interest rate- or inflation expectations is by far not an easy task, both because of its technical complexity and the assumptions which often remain implicit in the process. The primary motivation of this paper is to present some methods by which the major technical obstacle, i.e. the estimation of the zero-coupon yield curve from couponbearing bond price data can be done, and also to evaluate these methods in terms of suitability to current Hungarian data and practical use in monetary policy. In addition to this, I would like to emphasize and make explicit some often overlooked assumptions (especially the expectations hypothesis) needed to draw conclusions about market expectations of future nominal rates and inflation. Using the estimated zero-coupon rates, I also try to quantify the average difference between yields-tomaturities (YTMs) of coupon bonds and the corresponding zero-coupon rates in Hungary. The structure of the paper is as follows: Section 1.1 and 1.2 describe the basic concepts and definitions related to the yield curve, and compare zero-coupon curves with yield-to-maturity curves, focusing on the theoretical shortcomings of the latter. Section 1.3 defines implied forward rates, and shows how to interpret them. Section 1.4 focuses on the conditions which are necessary to hold if one wants to infere nominal interest rate and inflation expectations from the zero-coupon yield curve. Part 2 deals with some methodological issues of the estimation of zero-coupon yield curves and compares alternative estimation methods on the basis of their applicability to Hungarian data and monetary policy purposes. Sections 2.1 and 2.2 give the descriptions of the two methods examined in detail in this paper, i.e. polynomial fit and “parsimonious” models. Section 2.3 deals with data issues that arise when we try to estimate yield curves using Hungarian bond price data. Section 2.4 lists some of the criteria which can be used to select a particular estimation method and (where it is possible) compares the methods applied to Hungarian data on the basis of these criteria. Section 2.5 contains the method proposed for future use in the NBH. Part 3 is an application of the estimated zero-coupon yields, which empirically demonstrates the bias in YTM-type yield curves when the underlying zero curve is non-horizontal. More specifically, in this part I try to quantify the inherent bias in the daily “benchmark yields” calculated by the State Debt Management Agency (SDMA).