Gaussian Estimation of a Two‐factor Continuous Time Model of the Short‐term Interest Rate

Abstract

This paper considers the econometric estimation of a two‐factor model of the short‐term interest rate. We develop a procedure for the time series estimation of its parameters, based on recently developed Gaussian estimation methods which are extended to handle unobservable state variables. The main methodological contribution is the derivation of an exact discrete model and the exact Gaussian likelihood function in terms of the discrete observations and structural parameters of the two‐factor model. The model is estimated on one month euro‐currency interest rate data for seven currencies – the Belgium franc, Canadian dollar, Dutch guilder, French franc, German mark, Italian lira, and the US dollar over the period February 1981 to December 1995 – and our results indicate that the method works well in practice. The empirical estimates reported in this study can be used to compare estimates from the calibration of an arbitrage‐free analogue of the model to market prices of interest rate caps and swaptions for use in the financial markets. (J.E.L.: C13, E43).