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).

Information in T-bill Auction Bid Distributions

In this paper UK data is used to compare two potential sources of information regarding market uncertainty about future short interest rates. One is the so-called risk-neutral density function (RND) derived from interest rate option prices, the other is the distribution of bids submitted to an auction of short-term Treasury bills. More specifically, time series of RND standard deviations and auction bid standard deviations are compared. The results suggest that in some periods the auction bid standard deviations co-moved with those of the RNDs. Thus, in principle, auction bid standard deviations may be useful to get a picture of market uncertainty about future short rates even in the absence of well-developed interest rate options markets. In the Supplement, encouraged by the above results, the author uses Hungarian T-bill auction data to check whether auction bid dispersion measures in Hungary make any sense as indicators of market uncertainty about future interest rates. Lacking any RND data for this country, this can only be done in indirect ways. These include looking at the correlations of auction dispersion measures of different T-bill maturities, comparing the time series of these measures and bid-ask spreads (another possible indicator of uncertainty) and conducting an intuitive consistency check for a certain time period.

The use of staff policy recommendations in central banks

The focus of this paper is on the use of staff policy recommendations in central banks. Based on the responses to a recent survey conducted by the Bank of International Settlements, the paper tries to answer two questions. (1) How (to what extent) do central bank decision-makers make use of staff views regarding the appropriate policy? (2) What institutional features determine the extent to which staff policy views are utilised by decision-makers? The ‘weight’ with which staff policy views are taken into account is proxied by how explicitly they are presented to the policy board. Based on the survey responses about how staff policy views are presented, a Staff Recommendation Explicitness Index (SREI) is constructed for each central bank surveyed. SREI is then regressed on a number of candidate explanatory variables. The results suggest that the use of staff policy views, proxied by SREI, is negatively related to the size of the policy committee. Furthermore, the use of staff policy views seems more pronounced if the committee is consensus-seeker and if the monetary regime is inflation targeting. Tentative explanations are offered for each of these findings.monetary policy, central bank staff, committee, decision-making

On the equivalence of linear sets

Let $L$ be a linear set of pseudoregulus type in a line $\ell$ in $\Sigma^*=\mathrm{PG}(t-1,q^t)$, $t=5$ or $t>6$. We provide examples of $q$-order canonical subgeometries $\Sigma_1,\, \Sigma_2 \subset \Sigma^*$ such that there is a $(t-3)$-space $\Gamma \subset \Sigma^*\setminus (\Sigma_1 \cup \Sigma_2 \cup \ell)$ with the property that for $i=1,2$, $L$ is the projection of $\Sigma_i$ from center $\Gamma$ and there exists no collineation $\phi$ of $\Sigma^*$ such that $\Gamma^{\phi}=\Gamma$ and $\Sigma_1^{\phi}=\Sigma_2$. Condition (ii) given in Theorem 3 in Lavrauw and Van de Voorde (Des. Codes Cryptogr. 56:89-104, 2010) states the existence of a collineation between the projecting configurations (each of them consisting of a center and a subgeometry), which give rise by means of projections to two linear sets. It follows from our examples that this condition is not necessary for the equivalence of two linear sets as stated there. We characterize the linear sets for which the condition above is actually necessary.Comment: Preprint version. Referees' suggestions and corrections implemented. The final version is to appear in Designs, Codes and Cryptograph

On sets of points with few odd secants

We prove that, for $q$ odd, a set of $q+2$ points in the projective plane over the field with $q$ elements has at least $2q-c$ odd secants, where $c$ is a constant and an odd secant is a line incident with an odd number of points of the set.Comment: Revised versio

A Carlitz type result for linearized polynomials

For an arbitrary $q$-polynomial $f$ over $\mathbb{F}_{q^n}$ we study the problem of finding those $q$-polynomials $g$ over $\mathbb{F}_{q^n}$ for which the image sets of $f(x)/x$ and $g(x)/x$ coincide. For $n\leq 5$ we provide sufficient and necessary conditions and then apply our result to study maximum scattered linear sets of $\mathrm{PG}(1,q^5)$