Academic journal article Journal of Money, Credit & Banking

Testing Term Structure Estimation Methods: Evidence from the UK STRIPS Market

Academic journal article Journal of Money, Credit & Banking

Testing Term Structure Estimation Methods: Evidence from the UK STRIPS Market

Article excerpt

THE TERM STRUCTURE of interest rates defines the array of discount factors on a collection of default-free pure (zero-coupon) discount bonds that differ only in their time to maturity. It is used for a number of purposes. For example, it can be used to set the price of new issues of default-flee debt, to set the interest rates on intragovernmental loans, or to test the theories of the stochastic evolution of the term structure (e.g., Cox, Ingersoll, and Ross 1985).

The prices of government bonds, known as gilts in the United Kingdom, are generally used in the estimation of the term structure of interest rates. Following the introduction of the gilt STRIP facility in December 1997, which permitted the separate trading of the cash flows of a selection of conventional (coupon-bearing) gilts, direct observation of the term structure of interest rates became possible. The yield to maturity on a stripped cash flow, which is its per period average rate of return until maturity, defines the unique default-free interest rate for that maturity. Unless there exists a continuum of zero-coupon bonds across the maturity range, however, there will be a need to use some form of interpolation method whenever interest rate estimates are required for dates that do not coincide with existing cash flows. The aim of this study is to compare a selection of interpolation methods in the case of the UK gilt STRIPS market.

Interpolation methods were introduced into the term structure literature long before zero-coupon bonds were first traded. At that time, it was necessary to use coupon-bearing bonds to estimate the term structure, and the use of interpolation methods met twin objectives. In addition to the desirability for interpolation, the use of such methods would, in many cases, make estimation feasible. In the absence of arbitrage, the prices of all coupon-bearing bonds, [P.sub.i], are related to the zero-coupon yield (spot interest rate) curve, [y.sub.t], by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

where the discount function, d(t) = exp(-ty(t)), is the price of a unit payoff at date t and where bond i pays a periodic coupon at rate [c.sub.i] and repays its face value, [F.sub.i], at date [n.sub.i]. If the number of bonds equals the number of payment dates, the term structure can be exactly identified by solving equation (1) simultaneously for all bonds. In the case where there are more bonds than payment dates, equation (1) is overidentified, but an approximate fit can be obtained by using, for example, least squares. Carleton and Cooper (1976) successfully employed this method by selecting a sample of around 30 bonds that only incurred four payment dates per year and had a maximum maturity of 7 years. In most bond markets, however, the number of payment dates greatly exceeds the number of bonds available, and so some means of reducing the dimensionality of the term structure (to less than the number of bonds) is needed. The solution, first suggested by McCulloch (1971), is to approximate the term structure with a low-dimensional function, which depends on a small number of parameters. This function, being defined across the maturity spectrum, simultaneously undertakes the interpolation task.

Since the pioneering work of McCulloch (1971, 1975), a huge literature has grown up devoted to both innovating and comparing alternative approximation functions. (1) With few exceptions, this literature has used coupon-bearing bonds to conduct the empirical analysis. With coupon-bearing bonds the comparison of alternative approximation functions is made a more complex task as the functions are both making the estimation feasible and providing the interpolation service. With zero-coupon bonds, estimation of at least some points along the term structure is always feasible, and so the approximation function is only providing the interpolation service. The feasibility and interpolation benefits from the use of approximation functions do not arise without a cost. …

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