A discrete time model of convergence for the term structure of interest rates in the case of entering a monetary union

This paper presents a method for constructing the term structure of interest rate spreads for two currencies in the context of a country's entry into a monetary union. We propose a special type of process that ensures the convergence of the short-term interest rate spread to zero by a fixed moment in time, which we call the discrete-time Brownian bridge process. Using this process and the conventional pricing kernel framework, we derive double recursive formulas for computing the affine coefficients for the term structure of interest rate spread. The estimated model counterpart, which is based on the pre-EMU interest rate spread data for the interest rates of the German mark and Italian lira, fits the data reasonably well and captures the stylized empirical facts. Namely, spreads for all maturities have downward trends, and the longer the maturity is, the less spread there is.