• CSA
• libor
• euribor
• eonia
• basis swap
• forward rate
• FRA
• overnight indexed swap
• OIS discounting
• multiple-curve framework
• single-curve framework
• Interest rate derivatives
• collateral
• forward curve

The financial crisis begun in the second half of 2007 has caused, among many well-known consequences, a radical evolution phase of the classical interest rate derivatives pricing framework. Clearly this is not what common people care about after the sub-prime crisis, but is instead something that caused many problems for academics and practitioners. In fact, contrary to what the markets believed just few years ago, some issues, like credit and liquidity risk, that were before regarded to be negligible and then ignored, were found to have an important impact on the prices of financial instruments.
In fact, since August 2007, with the sub-prime crisis that has spread a stronger perception of the credit and liquidity risk present within the financial markets, primary interest rates of the interbank market, e.g. Libor, Euribor, Eonia, and Federal Funds rate, started to display large basis spreads, in some cases on the order of hundred basis points and even more. Similarly, some other relations which constituted a milestone in finance broke down. In fact, the well-known correspondence between FRA rates and forward rates implied by two consecutive deposits now does not hold any more. Another evident consequence is the sudden and significant explosion of the basis swap spreads, which highlights a segmentation in the interest rate market, which is now evidently tenor-dependent.
In other words, some basic relations described on standard textbook have been called into question, with some other relevant consequences on the way an interest rate derivative has to be priced.
In fact, the above-mentioned old consistencies between rates allowed the construction of a single curve to be used both as a discounting curve and as a forward curve, which made the pricing process of a, say, interest rate swap very straightforward and simple from a computation point of view.
Failing these relations, the financial community has thus been forced to start the development of a new theoretical framework aimed at taking into account the new market information. In other words, the interest rate market has undergone nothing short of a revolution.
As a consequence, the above-mentioned structural changes have determined the necessity to construct not just one yield curve to use both as an interest rate generating curve and as a discounting curve, but as many curves as the underlying rate tenors are in order to generate the future cash flows, and another curve to discount the cash flows themselves (the so called “discounting curve”). This has determined a structural transition from the so called “single curve approach” to the so called “multiple curve approach”, with lots of implications both for practitioners and for academics.