Assume a CDS buyer and a seller enter into an agreement. The buyer makes payments to the seller and no credit event takes place.
Does the buyer then get the face value of the bond back at its termination? (Can I assume that very CDS buyer has ownership of a bond?)
You cannot assume that the CDS buyer owns the bond. Many don’t. That was the big problem for AIG.
If there’s no default, then a bondholder will get a final payment of principal plus coupon. You know this from Fixed Income at Level I and Level II. Whether the bondholder buys protection or not doesn’t change that.
Also note, that in order to BUY protection, you actually are SHORTING a CDS.