7.1 Introduction

The yield curve represents the relationship between the discount rates on a collection of default-free future cash flows, such as the coupon and redemption payments on UK government bonds, which differ only by their due date. By providing a spectrum of interest rates across future time horizons, the yield curve contains information regarding the whole market's expectations of future events, which is valuable for macroeconomic policymakers. In the UK government bond market, as in all bond markets, the cash flows to bondholders are made at regular but infrequent intervals. For a policymaker interested in a particular future date that does not happen to coincide with a cash flow date of a bond, there will be no directly observable discount rate. As a result, techniques have been developed to estimate the whole yield curve from the set of available bonds.

It is typical in bond markets for the set of future cash flow dates to far exceed the number of bonds, so giving rise to an under-identification problem when attempting to estimate the yield curve, as there are fewer known bond prices than unknown discount rates. The solution, first suggested by McCulloch (1971), is to approximate the yield curve with a low-dimensional function of maturity (the due date of the cash flow), which depends on a small number of parameters. By fixing a functional form for the yield curve, it also becomes possible to interpolate between observed maturities to obtain an estimate of the entire continuum of yields.