et
be a fixed CDS coupon schedule. It makes sense to introduce a coupon
that sets market value of a CDS to zero given market conditions at time moment
.
The
is a stochastic process.
Based on the
relationship
we
obtain
The expression in the numerator is a price of combination of risky annuities.
We can use it as a numeraire as long as there is no default. Hence, there
exists a probability measure such that the
is a martingale.
We represent the price of the CDS using the quantity
:
Hence, we replace a nonobservable quantity
with the directly quoted quantity
.
We introduce the
notation


(Risky annuity)

and write the last result as
