Yield curve fitting with term structure models: Empirical evidence from the euro market

We study the fitting of the euro yield curve with the Longstaff and Schwartz (1992) (LS) two-factor general equilibrium model and the Schaefer and Schwartz (1984) (SS) two-factor arbitrage model of the term structure of interest rates. The Cox, Ingersoll, and Ross (1985b) (CIR) one-factor model is also studied as a reference. LS use the short-term interest rate and the volatility of the short-term interest rate as state variables while SS use the spread between the short-term and the long-term interest rate and the long-term interest rate. Thus, the LS model should perform better (worse) than the SS model in pricing short-term (long-term) securities. Moreover, since the CIR model can be nested into the LS model, we expect the latter model to perform better than the former. The results show that, as expected, the LS model is best adjusting to the short-term yields. Surprisingly, the CIR model is best fitting to long-term yields. In any case, the three models have difficulties matching both the entire yield curve and the term structure of volatilities.