he expression
located in the denominator of the (
Swap rate
) is a
linear combination of prices of traded instruments. It is always positive.
According to formula (
Suitable numeraire
),
may be taken as a numeraire. The probability measure associated with the
numeraire
is called the "swap measure". The numerator of the formula
(
Swap rate
) is also a price of a traded instrument.
Therefore, the quantity
is a martingale under the swap measure.
One may justify use of BlackScholes formula for pricing of swaption using the
notion of swap measure. Indeed, price of swaption is given
by
We arrived to the BlackScholes situation if
is assumed to be lognormal.
