A class of arbitrage-free log-normal-short-rate two-factor models

An arbitrage-free two-factor model is presented, which is driven by the short rate and the consol yield, and which ensures log-normal short rate and positive rates. The market price of an arbitrary (discrete) set of discount bonds is recovered by construction, and an arbitrary degree of correlation can be accommodated between the long yield and the spread. By virtue of its Markovian nature, the model can be mapped onto a recombining tree, and therefore readily lends itself to the evaluation of American and compound options, which are difficult to evaluate with non-Markovian log-normal forward-rate models such as HJM. Comparison with such a two-factor HJM model has given good agreement in so far as the pricing of one-look triggers is concerned. The calibration to caplets and European swaptions is discussed in detail.