A bank hedging an interest rate swap with a credit default swap?

Interest rate swaps and credit default swaps hedge entirely different risks.

In your example, the bank receives a fixed rate on a loan for 6.5%, but pays 6.45% to a dealer. The dealer will then pay a floating rate (i.e. the "swap rate") to the bank, which depends on the time to maturity and current interest rate environment. The bank in this case wants to take the opportunity to benefit from a rise in interest rates (since it now receives floating from the dealer) but will accept the risk of interest rates falling (which is generally acceptable for a bank, which has mostly floating-rate liabilities).

To hedge credit risk, the bank will buy a credit default swap from another dealer, and the pricing has nothing to do with the interest rate swap. It will be related to the credit risk of firm "A". Let's say that the 6.5% loan is 200 basis points over treasuries (i.e. a treasury bond maturing at the same time yields 4.5%). The bank will probably have to pay about 2% (the amount of the spread) to another dealer to hedge the risk of the loan, since most of this spread relates to the credit rating of company "A". If company "A" defaults, the CDS dealer must pay the bank off. If "A" pays off the loan, the dealer keeps the 2% payments.

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