In this paper we study the convergence model of interest rates by Corzo and Schwartz. It models the situation when a country is going to enter a monetary union, for example the eurozone. We are interested in estimating the underlying short rate, which is a theoretical variable, not observed on the market. We use the procedure already employed for the Vasicek model to the eurozone data and for the case of a zero correlation we show that a similar procedure can be used also for the estimation of the domestic parameters and the short rate values. The assumption of the zero correlation allows us to simplify the optimization problem, but using simulations we show that our algorithm is robust to the specification of the correlation. It estimates the short rate with a high precision also in the original case of a nonzero correlation, as well as in the case of a dynamic correlation, when the correlation is modelled as a function of time. Finally, we use the algorithm to real market data and estimate the short rate before adoption of the euro currency in Slovakia, Estonia, Latvia and Lithuania.

Short rate models of interest rates are formulated in terms of stochastic differential equations which describe the evoution of an instantaneous interest rate, called short rate. Bonds and other interest rate derivatives are then priced by a parabolic partial differential equation. We consider two-factor models, in which also correlation between the factors enters the bond-pricing differential equation. Firstly, we study the dependence of the bond prices on the correlation in three particular short rate models. The differences and common features of the results motivate us to investigate the dependence of the solution to the bond-pricing partial differential equation on the parameter representing correlation between the factors in a general case.2010 Mathematics Subject Classification. Primary: 35K15; Secondary: 35Q80. 90Effect of correlation on bond prices in short rate models