The Special Case of AAA-Rated Institutions

We will finish the discussion on curve construction with the special mention of AAA-rated institutions, a category to which many development institutions belong. It is not uncommon for AAA-rated institutions not to post collateral and not to pay interest on the collateral paid to them. This arrangement is often referred to as one way CSA (CSA stands for Credit Support Annex, which appeared in the ISDA 1994), in the sense that, unless both parties are AAA, the rules of collateral apply only to one of the two. In most cases they do not have access to central bank windows for borrowing.^[1] What does that mean in terms of curve construction? This is a very interesting question, which at the time of writing is at a center of a discussion that involves not only the move of swaps toward clearinghouses, but also the implication of the Dodd-Frank Act (a piece of U.S. legislation whose goal is to bring transparency, stability, and, hopefully, safety to the financial world). For consistency with all that has been said above, the view should be that AAA-rated institutions should not move toward OIS discounting. We have said that the discounting choice for an institution should be driven by the borrowing level of the institution itself and the rate of growth of the collateral received and paid. All of these arguments point to remaining a LIBOR-driven discounting. Of course this view is only one side, let's call it the funding view, of the current debate on discounting (see Hull and White [48] and Morini and Prampolini [64] for the original point and the reference section for the subsequent ones in the debate). This debate concerns the so- called FVA, or the Funding Value Adjustment, that needs to be applied to discounting in order to take into account differences in funding levels between counterparties. The other side, let's call it risk-free view, of the debate claims that funding levels should not have any input at all and discounting should only be done on what the market deems to be the current risk-free rate. This is because the risk-neutral framework, by which we all still abide, requires derivatives to be discounted at a risk-free rate. This rate is certainly not LIBOR at the moment, and the rate that would qualify as risk free is indeed the OIS rate. This is slightly different from the way we introduced OIS. In fact, the risk-free view believes in using OIS but not because it is the rate at which collateral grows (the way we introduced it), but because it is a form of risk-free rate. The risk-free view would then hold that a AAA institution, like everyone else, irrespective of its collateral and/or funding situation, should discount using the OIS rate. (Incidentally, this would prepare such institution for a future move toward central clearing.) In this book we do not believe that collateral and funding should be ignored, because we try to follow an argument by which the widest possible view of an institution's activities should be considered when valuing financial instruments. Nonetheless, we admit that no easy solution exists to the debate we have just mentioned and both sides have made valid arguments. Let us, however, move away from this debate and discuss an interesting side effect of the special situation in which a AAA institution finds itself.

We have seen how swap pricing is not a solitary activity but involves at least two parties, and now, with the move toward clearinghouses, three. What does the perfectly understandable decision on the part of AAA-rated institutions to remain with LIBOR-driven discounting entail in the wider financial system? Operationally speaking, a financial institution chooses the type of discounting according to the counterparty. Because each counterparty can post collateral in one of several currencies,^[2] a financial institution's curve construction system needs to be able to assign to counterparty ABC a curve construction driven by an X OIS curve. The association of a certain AAA party to a LIBOR-driven curve construction would be just another pairing. As far as clearing is concerned, however, unless there will be a special provision to keep trades involving AAA institutions over the counter, that might be more of a problem for which at present there does not seem to be a clear answer.

Let us finish with a brief change of perspective and imagine we are facing a AAA institution. Let us imagine that we trade a fix for floating swap with principal N in a generic currency such that we define the present value of the fix leg

and the present value of the floating leg

Let us imagine the situation in which we are receiving fix and paying floating, meaning that the MTM of the swap is for us given by

If the MTM is negative, meaning we need to post collateral, we will be receiving nothing in the sense that no interest will be paid by our counterparty, the AAA institution, on that amount. Instead, we will be paying overnight rate / to borrow the collateral we need to post. Should the MTM

be positive, we will be receiving LIBOR (not from the counterparty but from the fact that we will be in the position to lend it at LIBOR). In practice

(2.19)

where 1X is the unit function, equal to one if X is true and zero otherwise. Note that Equation 2.19 shows the situation at a specific moment in time. As we have said previously, collateral calculations are daily exercises, meaning that the above will be summed over a whole payment period. In Equation 2.19 we see a discontinuity, a function that goes in a nonsmooth way across a single point (or, one could say, a function that is nondifferentiable at the point MTMt = 0). Whenever we see a situation like this, we know that there should be special hedging involved, in this case made even more special by the underlying itself. Banks trade CSA options to hedge structures like these arising from special collateral agreements (which we have defined previously as one-way CSAs).^[3] We should note that the situation presented in Equation 2.19 is interesting because we have simultaneously two different exposures to LIBOR. This is particularly easy to see when it is in the money (i.e., MTMt > 0): we are short LIBOR in the swap itself (if it decreases we pay less and therefore the MTM increases in our favor), but we are long LIBOR as far as the income we receive from investing the MTM amount itself.

The example above, although it might appear too specific for the general tone of the chapter, was mentioned nonetheless to show that one should try to take into consideration the biggest possible picture of the activities of an institution, from borrowing to hedging, in order to make the correct pricing choices.

• [1] In the United States for example, the Fed Fund window is a borrowing facility that has always been opened to commercial banks and not to investment banks (hence the need of the latter to borrow at LIBOR). With the move to commercial bank status, on September 18, 2008, on the part of Morgan Stanley and Goldman Sachs, all investment banks now have access to the window. Note: The access is not for all activities; the majority of funding for an investment bank still comes from LIBOR- level borrowing.
• [2] Sometimes a party has the option to switch collateral currencies, creating interesting situations (see Whittall [84]).
• [3] One needs to point out that it is not only AAA-rated institutions that do not post collateral. There are other entities, usually corporates, that might have agreements in which they do not pay collateral. The counterparty risk is then taken care of through Counterparty Value Adjustments (CVA), which we shall mention briefly in Section 7.3.2. We have reached the point where any discussion about discounting moves into explicit credit risk management. This is beyond the scope of this book and in particular beyond the scope of this chapter.