Model Dynamic
The LIBOR market model models a set of forward rates, as lognormal processes. Under the respective -Forward measure
Here, denotes the forward rate for the period . For each single forward rate the model corresponds to the Black model. The novelty is that, in contrast to the Black model, the LIBOR market model describes the dynamic of a whole family of forward rates under a common measure. The question now is how to switch between the different -Forward measures. By means of the multivariate Girsanov's theorem one can show that
and
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