Zero-coupon yield curves: technical documentation

BIS Papers  |  No 25  | 
30 October 2005


Following a meeting on the estimation of zero-coupon yield curves held at the BIS in June 1996, participating central banks have since been reporting their estimates to the Bank for International Settlements. The BIS Data Bank Services provide access to these data, which consist of either spot rates for selected terms to maturity or represent estimated parameters from which spot and forward rates can be derived. In the case estimated parameters are reported, the Data Bank Services provides, in addition to the parameters also the generated spot rates.

The purpose of this document is to facilitate the use of these data. It provides information on the reporting central banks' approaches to the estimation of the zero-coupon yield curves and the data transmitted to the BIS Data Bank. In most cases, the contributing central banks adopted the so-called Nelson and Siegel approach or the Svensson extension thereof. A brief overview of the relevant estimation techniques and the associated mathematics is provided below. General issues concerning the estimation of yield curves are discussed in Section 1. Sections 2 and 3 document the term structure of interest rate data available from the BIS. The final section provides examples of estimated parameter and selected spot and forward rates derived thereof. A list of contacts at central banks can be found after the references. The remainder of this document consists of brief notes provided by the reporting central banks on approaches they have taken to estimate the yield curves.

Since the last release of this manual in March 1999 there have been four major changes: Switzerland started to report their estimates of the yield curve to the BIS in August 2002. Furthermore, Sweden began to use a new estimation method in 2001, the United Kingdom since September 2002 and Canada since January 2005. These changes are included in Tables 1 and 2.