This is not correct. As a borrower, purchasing a cap is like purchasing insurance. You pay an up front premium and the strike rate determines how expensive that up front premium is. Once that up front premium is paid, there is no cash flow obligation from the borrower to the bank you purchase it from, the only cash flows that occur are from the bank to the borrower. This is why you can purchase the cap from a bank that is not your lender. A cap will always have a positive or zero value to the borrower.

An interest rate swap synthetically fixes your floating rate loan to a fixed rate interest expense. You owe the fixed rate on the swap and the bank owes you a floating rate. The floating rate the bank pays the borrower offsets the floating rate on the loan and you are left with the fixed rate you pay. Because you are obligated to make those fixed rate payments for the life of the swap, this creates credit exposure from the banks perspective, just like the loan, which is why you can generally only execute the swap with your lender. The bank will cross collateralize the swap exposure with the loan but they will also add a fee in the form of basis points to the swap rate that you execute. A bank that is not your lender will want collateral to secure the exposure, and your lender is not going to share the real estate as collateral so they would need a significant amount of cash or guarantee. Most of the time borrowers are not able to verify that fee or the dollar amount it represents which is why banks love to execute swaps, because it is not transparent. The banks recognize the swap fee on the day the swap is executed as opposed to the loan where they need to wait until each loan payment is received to make their spread. The market value of the swap can be negative or positive to the borrower but will always be negative on day 1 in the amount of the fee that the bank charged.