A 3-Factor Model for the Yield-Curve Dynamics - The Case of Stochastic Spot-Rate, Market Price of Risk and Volatility

This paper proposes a new 3-factor model for the dynamic in the yield-curve which belongs to the Affine class of term structure models. Using a yield-factor approach combined with a maximum likelihood estimation technique we conclude the following using Danish bond data over the period 2 January 1990 - 30 June 1998:1: We find all the parameters to be significant and when comparing the model generated interest rate series against the actual (observed) interest rate series we find for all maturity dates that we cannot reject the hypothesis that both samples have been randomly selected from the same distribution.2: We also find that there is a high degree of correlation between the predicted interest rates and the observed interest rates - given the state-variables.We also analyse the implied state-variables - that is the state-variables that arise when converting the model into a yield-factor model - and find that there are three dominant factors that govern the dynamic in the term structure of interest rates which can be recognized as, a Short-factor (sometimes called a Steepness-factor), a Level-factor and a Curvature-factor. This is in line with what is generally reported in the literature, see among others Litterman and Scheinkmann (1991).As is generally the case we also find evidence that the Level-factor is close to being nonstationary