Brace, Gatarek and Musiela Model

All the models examined thus far have been based on instantaneous short-term or forward interest rates. This implies that the fundamental building blocks, that is default-free bonds, are assumed to be continuous (or smooth) with respect to the tenor. Even the discrete time models such as Ho and Lee [27] (see Chapter 10) and Black, Derman and Toy [6] (see Chapter 8), which make use of a discrete set of discount bonds, assume these are extracted from an underlying continuum of default-free bonds. Such a continuum of default-free discount bonds is not actually traded, nor does the associated continuum of instantaneous shortterm or forward interest rates exist.