As corporations continue to issue bonds, some choose to convert their fixed rate liabilities into a floating rate. The reason is that LIBOR has fallen to historically low levels. For corporate treasurers it's worth taking interest risk in order to 1-month or 3-month LIBOR plus spread.
For example if a company issues a 7% coupon 10-year bond, it can swap it into floating rate by receiving fixed on a swap (at 3.8%) and paying LIBOR. That converts their liability from 7% to LIBOR + 3.2% (7 - 3.8 = 3.2). With 3-month LIBOR currently at 0.43% the financing cost becomes 3.63%. Of course if at some point in the future, LIBOR goes to 6%, the cost will jump to 9.2% - but that's a risk worth taking for some. Some corporations think that if LIBOR increases significantly, the economy is supposedly doing better (otherwise the Fed would keep short-term rates low), and the company should be able to afford higher coupon payments.
But what about the bank that enters into that swap? It turns out that with the forward LIBOR curve as steep as it currently is (see chart below - the curve is significantly steeper than 3 months ago), the bank is taking more credit risk. If rates do what the forward curve is predicting, then in the earlier years the bank is a net payer to the company (red arrow on the chart below) . In the later years when forward LIBOR is higher than the locked in swap rate (purple line on the chart below), the bank is a net receiver of cash (blue arrow).
Well if the bank is first a net payer and then in later years it's a net receiver, this is effectively a loan to the company. Now rates never actually follow the forward curve, but that's the starting point for assessing the bank's credit exposure. The steeper the curve, the larger the effective "loan" (initial outflows), the more credit risk. The bank then runs a simulation on how volatility may impact rates to measure a "stress scenario" exposure (sometimes called "potential exposure"). If this exposure is large enough, the bank will sometimes purchase a credit default swap on the company. If rates go high enough, the company will owe the bank increasing periodic payments, and if the company fails to make those payments, the bank can use its CDS position to reduce or eliminate losses.
Of course CDS costs money, and depending on the company's credit quality, the bank will add spread to the swap they do with them. In the example above, rather than transacting the swap at 3.8%, the bank will agree to pay say 3.6%, making the company's financing expenses LIBOR + 3.4%. And the steeper the curve gets, the higher this spread will become. As LIBOR stays low and the credit markets stay open, the demand for these swaps continues to stay strong.