Interest rates and bonds

The estimation of the parameters of the CIR-2 model and detailed description of the used methods are subject of several existing articles, e.g. Chen and Scott (1993), Duan and Simonato (1999), Bolder (2001), Beletsky and Szimayer (2002) and Fischer, May and Walther (2003). The problem is not trivial. The most efficient method seems to be maximum-likelihood estimation with Kalman-filtering. In particular, we used the machinery as explained in Fischer, May and Walther (2003). The interested reader can find further information in this paper and the references therein.

A comment on the data: We use the historical yield structure of the German debt securities market (monthly, taken at the end of each month). The values for spot rates with maturities $\tau>0$ up to 28 years can be computed via a parametric presentation of yield curves (the so-called Svensson-method; cf. Svensson (1994) and Schich (1997)) for which the historical parameters can be taken from the homepage of the German Federal Reserve (Deutsche Bundesbank; http://www.bundesbank.de). The implied Bundesbank values $R'$ are estimates of discrete interest rates on notional zero-coupon bonds based on German Federal bonds and treasuries (cf. Schich, 1997) and have to be converted into continuous interest rates by $R = \ln (1+R')$.