Interbank yield curve

In this chapter, we perform a factor analysis of the zero-coupon euro interbank yield curve, and also of zero-coupon Treasury yield curves from five individual countries, France, Germany, Italy, Spain, and the Netherlands, so as to isolate the key aspects of the dynamics of term structures of interest rates in the Eurozone. 

We compute PCA with the zero-coupon euro interbank yield curve for the period from 2 January 2001 to 21 August 2002. We use zero-coupon rates with 17 different maturities from one month to ten years. The basket of inputs contains three kinds of instruments money... 

PCA OF THE 1REASURY AND EURO INTERBANK YIELD CURVES IN THE EUROZONE ... 

We now apply the methodology just described to study the dynamics of the Treasury yield curve for selected individual countries from the Eurozone, as well as the dynamics of the Euro Interbank yield curve. 

PCA of the Interbank yield curve. Because they do not apply to the same variables, it should be expected that results obtained with the Interbank yield curve be different from results obtained with Treasury yield curves. This is confirmed by the numbers in Exhibit 24.1. The first factor only accounts for 47.54% of the interest rate changes, while the second factor explains 25.63%. The inferior percentage of explanation by the first factor can be related to the fact that eight out of the 17 variables we use relate to the short-term segment of the curve. The three first factors account for 84.08% of the yield curve deformations while the first five factors account for 93.34%, which means that residuals are not negligible. 

We now compute the correlation between factor 1 (as obtained from PCA) of the different Treasury yield curves and the Interbank yield curve. We do the same for factor 2 and factor 3. Results are first detailed for the whole period, and then on each year (see Appendix C of this chapter). 

Least-squared methods used to derive the current interbank curve are very similar to those used to derive the current nondefault Treasury curve. After converting market data into equivalent zero-coupon rates, the zero-coupon yield curve is derived using a two-stage process, first writing zero-coupon rates as a B-spline function, and then fitting them through an ordinary least-squared method. 

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