A Three - Factor Convergence Model of Interest Rates ∗

A convergence model of interest rates explains the evolution of the domestic short rate in connection with the European rate. The first model of this kind was proposed by Corzo and Schwartz in 2000 and its generalizations were studied later. In all these models, the European rates are modelled by a one-factor model. This, however, does not provide a satisfactory fit to the market data. A better fit can be obtained using the model, where the short rate is a sum of two unobservable factors. Therefore, we build the convergence model for the domestic rates based on this evolution of the European market. We study the prices of the domestic bonds in this model, which are given by the solution of the partial differential equations. In general, it does not have an explicit solution. Hence we suggest an analytical approximative formula and derive order of its accuracy in a particular case.