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 Sch-wartz (1992) (LS) two-factor general equilibrium model and the Schaefer and Schwartz (1984) (SS) two-factor arbitrage model of the term structu-re of interest rates. The Cox, Ingersoll, and Ross (1985b) (CIR) one-fac-tor 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 ex-pect 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. Key words: term structure, yield curve, calibration. JEL classification: C21, C22, E43, G13. T here are three approaches to price contingent claims when the evolution ofinterest rates is stochastic. The arbitrage approach derives a partial diffe-rential equation (PDE) for the value of any contingent claim by construc-ting portfolios of securities whose weights are chosen to make the rate ofreturn on the portfolio non-stochastic. Then, to avoid the possibility of arbi-trage profits, the rate of return on the portfolio is made equal to the instantaneous riskless rate of interest. Examples of this method are the one-factor models of