he vanilla swap agreement has positive cashflows at times
calculated as
and negative cashflows at times
calculated as
where
 .
The number
is some predetermined fixed rate. The swap rate
is the particular value of the parameter
that makes such contract of zero value at the time
 .
Hence, the
is defined by the
relationship  
Since
is a martingale with respect to the
 -forward
measure we
continue
Hence,
Observe
that 
Therefore, | | (Swap rate) |
It is useful to express the price of the swap with any parameter
through the swap rate. Similarly to the above computations we
have   
|
