e are considering a debt structure
with payment dates
We introduce the following
notation


(Libor2)

We introduce the probability measure
associated with the price
taken as a numeraire,
.
The
is an increment of the
th
standard Brownian motion under the
.
It is the assumption of the model that the process
is
lognormal
under
for any
,
where the
are some deterministic functions. The increment
,
,
has a drift under
The calculation of
is our next task. According to the formula
(
Change of drift recipe
1
)
By the definition (
Libor
definition
),
Hence, for
,
We use the formula
(
Change_of_drift_recipe_1
),
Therefore
where the
are correlations and
are volatilities of the forward
rates
Similarly, for
,
LIBOR market model introduces a curvedependent drift. Hence, it has a state
variable (=description of filtration) of high dimensionality.
