Let say, I have some floating rate bond
where the coupon depends on 6-month Libor
with semi-annual payments.
In a typical text-book, the way this bond is priced (dirty-price) is that, replace expected future Libor rate
as Forward 6-month Libor rates
and then discount those cash-flows with Libor
rate again, using same Libor term-structure as seen today.
I feel this makes sense based on the T-forward measure
.
Now let say, this Bond is Corporate bond
. In this case, how does it make sense to discount it using Libor
? Should not we use different term-structure of Yield
based on the Credit-Rating
? But in that case, how to mathematical basis of using T-forward measure
would still hold?
Or, we should still use the Libor
as discounting and then make Credit-value adjustment
after I get the risk-free pricing using Libor? In that case, how should I calculate the Credit-value adjustment
for this case?
Really appreciate for any help to understand the mathematical basis for risky floating rate bond pricing.