Do we in practice have that floating rate bonds trade only at par?
How is credit spread included in floating rate bonds in practice? The way I see it is two possible ways.
The first is that we have a case of floating rate bonds that pays coupons that are calculated by a benchmark rate $r_i$, so that each coupon is for example $Nr_i/K$, where $N$ is the face value of the bond and $K$ is the number of coupons each year, and the last payment is $N(1+r_i/K)$. Then the price of the bond is lower than par at the reset date, it is lower than what you would get if you got this cashflow from a secure insitution. Do these types of bonds exist in the real world?
The second type would be a bond that at each coupon date pays $N(r_i/K+s)$, where $s$ is something you get extra, and at the last payment you get $N(1+r_i/K+s)$. And then these are priced at par at the reset date. Do these type of bonds exist in the real world?