Abstract
The maximum likelihood method is known to be efficient at estimating fully parametric models. One-factor short-rate models belong to this class, but surprisingly the maximum likelihood method is not extensively used for estimating them.
We believe it is a consequence of the current method's failure to determine the value of the short rate without justifying the calculation procedure, which often leads to a poor fit of the observed curve, making it difficult to interpret. In this paper, we propose a way to consider all observed yields at one time and extract the value of the short rate jointly from the entire yield curve.
This could be done thanks to a general description of the construction of the likelihood function of a time series of observed yields. The method identifies the models under the real-world measure and hence it is suited not only for pricing, but also for prediction of interest rates.
We illustrate the use of such an approach on the popular Hull - White model.