Interest rate swaps (IRS) are contracts in which two counterparties agree to exchange a sequence of interest payments on some notional amount of currency. In an overnight index swap (OIS), payments based on a fixed rate of interest are exchanged for payments based on a floating, overnight rate, which changes daily with market conditions. The swaps introduced in Chapter 2 are OIS, in which the floating rate is the Secured Overnight Financing Rate (SOFR) defined and discussed in Chapters 10 and 12. A fixed‐for‐floating swap is similar, but the floating rate is a term rate, rather than an overnight rate. Euribor swaps are fixed‐for‐floating swaps, in which the floating rate is typically the three‐month Euribor rate described in Chapter 12. Historically, the most common IRS across currencies were fixed‐for‐floating London Interbank Offered Rate (LIBOR) swaps, in which the floating rate was LIBOR of some term. However, with the transition away from LIBOR, as described in Chapter 12, these swaps are disappearing. OIS and fixed‐for‐floating swaps are the main focus of this chapter.

There are several classes of derivatives closely related to IRS, including forward‐rate agreements (FRAs) (see Chapter 12), caps and floors, and swaptions (see Chapter 16). While traditionally not called “swaps” by the financial industry, these products are defined as “swaps” in the Dodd‐Frank Act, which can cause some terminological confusion. In any case, these products are discussed elsewhere in this book but are included in the market size statistics presented in this chapter.

The first section of this chapter describes the size of the IRS market and how various market sectors use swaps. The second section builds on the introduction of IRS in Chapter 2 and of short‐term rates in Chapter 12 to present more detail on cash flows, pricing, and risk metrics. The third section uses several examples and cases to illustrate how IRS are used to manage risk. The fourth section addresses the risk that a swap counterparty defaults on contractual obligations, that is, counterparty credit risk, and describes the posting of collateral or margin to mitigate this risk. The fifth section explains swaps clearing, through which the two counterparties to a swap legally face a clearinghouse instead of each other. The sixth section introduces basis swaps and basis swap spreads and explains how swaps that reference nearly risk‐free, floating‐rate indexes, like SOFR, are priced differently from swaps referencing other floating‐rate indexes.

13.1 MARKET SIZE AND PARTICIPANTS

Table 13.1 shows outstanding amounts of interest rate swaps.¹ Products include OIS, fixed‐for‐floating swaps, FRAs, interest rate caps and floors, and swaptions. Counterparties include all those that report positions to the US Commodity Futures Trading Commission (CFTC), that is, US entities, US subsidiaries of foreign entities, and foreign swap dealers that register with the CFTC so as to do business with US persons. The first column of the table divides these reporting entities into selected sectors. The second and third columns give the total long and short notional amounts in each sector. As explained in Chapter 2, the notional amount of a swap is the amount on which payments are based. And, to be consistent with bond terminology, “long” positions are those that increase in value when interest rates fall (e.g., receiving fixed), while “short” positions are those that increase in value when interest rates rise (e.g., paying fixed). Because every swap contract has one counterparty long and the other short, total longs must equal total shorts across the whole market. According to Table 13.1, the total notional amount of the market is $210.7 trillion. This is an enormous number compared to the sizes of markets as presented in Chapter 0: the total amount of debt and loans outstanding in the United States in Figure 0.4 is only $76 trillion. As it turns out, however, notional amount outstanding vastly exaggerates the size of the IRS market.

The fourth and fifth columns of the table give a long and short “five‐year equivalent” notional amount, which is the notional amount of five‐year swaps that has the same risk as the raw notional amount. The risk sensitivity of swaps is discussed in the next section, but say, for example, that one sector was long $100 million of 10‐year swaps, which have a DV01 of 0.090; that is, a one‐basis‐point decline in rates increases the value of the position by $100 million times 0.090/100, or $90,000. Say also that five‐year swaps have a DV01 of 0.045. Then, the actual swap position – $100 million of 10‐year swaps – has the same risk as $200 million of five‐year swaps, and its “five‐year equivalent” notional amount is $200 million. On the other hand, a position of $100 million two‐year swaps, which has a DV01 of 0.018, has a five‐year equivalent notional amount of $100 million times 0.018/0.045, or $40 million. Returning to Table 13.1, the total five‐year equivalents in the market are $137.1 trillion, which is significantly less than the total notional amount of $210.7 trillion. First, the options on swaps included here have lower risk than the risk of their underlying notional amounts.² Second, a large proportion of swaps have terms less than five years. In fact, because bond markets, like the US Treasury and corporate bonds markets, have maturities concentrated in the five‐ to 10‐year range, five‐year swap equivalents are better than raw notional amounts for comparing market sizes.

The sixth and seventh columns of Table 13.1 report entity‐netted notionals (ENNs), which net long and short five‐year equivalents that are denominated in the same currency between each pair of counterparties. For example, if Counterparty A is receiving fixed from Counterparty B on $100 million five‐year equivalents and simultaneously paying fixed to Counterparty B on $60 million five‐year equivalents, then Counterparty A is long $40 million ENNs against Counterparty B and, symmetrically, Counterparty B is short $40 million ENNs against Counterparty A. Summing long or short ENNs across all counterparty pairs in a sector or across the market as a whole gives the corresponding elements of the table. Total market ENNs are $16.1 trillion, which are much less than five‐year equivalents. As explained in the next section, participants in the IRS market often take off risk by taking on new, risk‐offsetting positions, not by unwinding existing trades. As a result, pairs of counterparties are often both long and short to each other, and their ENNs are much less than their five‐year equivalents. In any case, at $16.1 trillion, the size of the IRS market is comparable to that of other US fixed income markets, as reported in Chapter 0.

Swap dealers, whose business is to make markets in swaps, are very likely to accumulate both long and short positions with their clients and are even more likely to do so with swaps clearinghouses, which are the legal counterparties to all cleared trades. In fact, the reduction of dealers' approximately $100 trillion long and short five‐year equivalents to $9.3 trillion long and $7.6 trillion short ENNs accounts for most of the reduction of total five‐year equivalents to total ENNs. Significant reductions also characterize hedge funds, which are in the business of trading swaps, and banks, which, as described later, use hedged swap positions to facilitate their customer loan businesses.

The final column of Table 13.1 is just the difference between long and short ENNs, which reveals whether a sector, as whole, is long or short swaps. (Differences are not exact because of rounding.) There is probably too much variation across hedge funds and asset managers, with each entity pursuing its own investment strategies, to explain the signs of these sectors' net ENNs. Banks as a sector are short, perhaps as a result of hedging the interest rate risk of their mortgage assets, although, as discussed next, banks and other financial companies receive fixed to transform their long‐term fixed‐rate debt into synthetic floating‐rate debt. Pension funds and insurance companies are likely overall long, as discussed below, to hedge the interest rate risk of their long‐term liabilities. Finally, also as discussed presently, nonfinancial companies pay fixed both to transform their floating‐rate bank loans into synthetic fixed‐rate loans and to hedge the risk of increasing rates before anticipated sales of long‐term debt.

13.2 IRS CASH FLOWS AND ANALYTICS

Chapter 2 describes the cash flows and pricing of a SOFR swap, and Chapter 12 explains the difference between borrowing or lending at rolling overnight rates versus term rates. This section builds on those foundations.

Cash Flows of OIS versus Fixed‐for‐Floating Swaps

Figure 13.1 illustrates the cash flows of a $100 million three‐year 1.64% versus SOFR swap, which is an OIS, while Figure 13.2 illustrates the cash flows of a €100 million three‐year 0.36% versus six‐month Euribor swap, which is a fixed‐for‐floating swap. Both swaps settle on February 16, 2022, and both figures are from the perspective of the fixed receiver. The SOFR swap makes annual cash flows using the actual/360 convention on both its fixed and floating legs. Therefore, the fixed interest earned after each 365‐day year, from February 16, 2022, to February 16, 2023, and from February 16, 2023, to February 16, 2024, is . Similarly, the fixed interest earned after the 366‐day year from February 16, 2024, to February 16, 2025, is .³ The floating cash flow of the SOFR swap over a given year, as explained in Chapter 2, equals the daily‐compounded interest earned on $100 million at realized SOFR rates over that year. Because each year on this swap starts and ends on February 16, the relevant SOFR rates are those from and including February 16 of one year through February 15 of the next year. Furthermore, because SOFR on February 15 is not published until the morning of February 16 (see Chapter 12), swap counterparties are given until February 17 to make payments on both legs of the swap. This payment delay is indicated in the figure by the light vertical lines to the right of February 16 of each year and by floating payment arrows pointing slightly past February 16.

Fixed‐for‐floating swaps use realized term rates to determine floating‐rate payments. The payment frequency on the fixed leg of these swaps can be annual or semiannual, while the payment frequency on the floating leg usually matches the tenor of the index rate. Figure 13.2 illustrates the cash flows of a swap of a fixed rate of 0.36% against six‐month Euribor. The fixed side of this swap pays annually and follows the 30/360 convention. Recalling that there are always 360 “30/360 days” in a year, the annual payment on the fixed leg is simply €100 million × 0.36% × 360/360, or €360,000. The floating side of the swap follows the actual/360 convention and pays semiannually to match the tenor of the floating‐rate index, namely, six‐month Euribor. The rate used to determine each floating‐rate payment is the Euribor setting two business days before the beginning of the payment period.⁴ Because six‐month Euribor on February 14, 2022, was 0.46%, and because there are 181 days between February 16 and August 16, 2022, the first floating‐rate payment of the swap in Figure 13.2 is €100,000,000 × (0.46%) × 181/360, or −€231,278. This means that the fixed receiver actually receives €231,278 from the floating leg of the swap. Note that there is no payment delay in fixed‐for‐floating swaps, because the cash flows are known well in advance of each payment date.

13.3 USES OF INTEREST RATE SWAPS

IRS can be conceptualized in two ways: as a leveraged position in a bond (see Chapter 2) and as an exchange of interest payments. The first interpretation best explains the actions of market participants in increasing or decreasing their interest rate exposures. An asset manager deciding to pay fixed, either as a bet that interest rates will rise or as a hedge against the interest rate risk of a corporate bond portfolio, is more interested in the DV01 of the swap than in the particular cash flows being exchanged. The first three use cases described in this section – pensions, Greece, and Brunswick Corporation – fall into this category. The second interpretation of swaps best explains the actions of market participants wanting to alter particular streams of cash flows. In the asset swap transactions described in Chapter 14, the owner of a corporate bond specifically wants to substitute the receipt of bond coupon with the receipt of a floating rate plus a spread. The last two use cases described here – bank loans and synthetic floating‐rate debt – fall into this category.

Hedging Future Debt Issuance

This use case starts by describing a forward swap or a forward‐starting swap, with Figure 13.3 illustrating a three‐year swap, one year forward. Through this forward swap, one counterparty agrees to pay fixed and receive floating for three years starting in one year, while the other agrees to receive fixed and pay floating. Importantly, the fixed rate is agreed on as of the trade date.

Now consider a corporation that plans to sell $100 million of three‐year bonds, but in one year's time. Assume that the corporation will be able to sell these bonds at a rate 1.5% over the then‐prevailing three‐year swap rate, and that the current three‐year swap rate, one year forward is 1.0%. The corporation can then lock in a borrowing cost of by paying fixed today on $100 million of the 1.0% three‐year swap, one year forward. Table 13.2 shows how the hedge works. Say that, one year later, the three‐year swap rate has risen to 1.5%. The corporation then issues $100 million of three‐year bonds at 3.0% and receives fixed at 1.5% on a $100 million three‐year swap. The net interest from the existing 1.0% forward swap, which has become a three‐year swap, the debt issue, and the new swap is . Alternatively, say that, one year later, the three‐year swap rate has fallen to 0.5%. The corporation then issues at 2.0% and receives in a three‐year swap at 0.5% for the same net of . Essentially, if rates rise, the corporation pays more on its debt, but wins on having locked in payment of a now low rate on the forward‐starting swap. Conversely, if rates fall, the corporation pays less on its debt, but loses on having locked in payment of a now high rate on the forward‐starting swap.

3‐Year Swap Rate	1.5%	0.5%
Trade	Cash Flow	Cash Flow
Issue Debt	−3.0%	−2.0%
Receive Fixed	1.5%	0.5%
Pay Fixed on Fwd Starting Swap	−1.0%	−1.0%
Total	−2.5%	−2.5%

In practice, instead of receiving fixed on a new swap at the time of issue, the corporation can unwind the forward‐starting swap and apply its realized NPV to the debt issue. A positive NPV would reduce the higher cost of debt, perhaps by using that positive NPV as proceeds and selling less debt, while a negative NPV would increase the lower cost of debt, perhaps by selling more debt to pay off that negative NPV.

Debt issuers sometimes find that forward swaps are expensive to transact relative to spot‐starting swaps. In that case, an issuer might pay fixed in a spot‐starting swap on a notional amount set so the DV01 of the hedging swap matches the DV01 of the forward sale of corporate bonds. Hedges with spot‐starting swaps do entail some curve risk, however. For example, in the scenario of the previous paragraph, paying fixed on a spot‐starting three‐year swap leaves the debt, but not the hedge, exposed to changes in the one‐year rate, three years forward. And paying fixed on a spot‐starting four‐year swap leaves the hedge, but not the debt, exposed to changes in the one‐year rate. In any case, note that swap hedges protect only against changes in the swap rate. Any increases in corporate borrowing rates relative to the swap rate, which was assumed away in the example of the previous paragraphs, are clearly not hedged by swap positions.

The Brunswick Corporation, which manufactures boats and other products, planned to issue $300 million of fixed‐rate debt in mid‐2023. In January 2021, it entered into $150 million of forward‐starting swaps to hedge half of that issuance. Furthermore, it seems to have structured its hedges with various starting dates and maturities to account for uncertainty about the actual issuance dates. The treasurer indicated that the volume of hedges might increase over time as, presumably, the dates of issuance become firmer. In short, figuring out what needs to be hedged can be much more difficult than figuring out how to hedge.⁹

Bank Loans

Banks prefer to make floating‐rate loans to customers. First, from the perspective of asset–liability management, floating‐rate assets naturally hedge deposits, which are floating‐rate liabilities (and which constitute the overwhelming majority of bank funding). Second, as discussed in Chapter 14, floating‐rate loans are much easier to sell in the secondary market than are fixed‐rate loans. Many borrowers, however, want to lock in a fixed interest rate over some term of their borrowings. The reconciliation of bank and borrower objectives is achieved with IRS, as illustrated in Figure 13.4. The bank makes a floating‐rate loan to the borrower, on which the borrower pays a floating rate. At the same time, the bank receives fixed from the borrower and, in a back‐to‐back swap, pays fixed to a dealer. The net result for the customer is a fixed‐rate loan: paying floating on the loan is offset by receiving floating on the swap, leaving only the fixed payments on the swap. The net result to the bank is the original floating‐rate loan: the cash flows from the two swaps, by design, exactly offset each other. While many banks do facilitate their customer loan business as illustrated in the figure, with back‐to‐back swaps, some hedge the aggregate risk of their customer swap portfolio with relatively few larger swaps.

Synthetic Floating‐Rate Debt

As just discussed, banks borrow at floating rates through deposits and make floating‐rate loans. Banks usually do want some amount of long‐term funding, however, because an overreliance on short‐term funding creates a vulnerability to withdrawals of that funding, either because of generally stressed financial conditions or because of concerns with that particular bank. A bank might, therefore, choose to issue some long‐term, floating‐rate debt, thus obtaining some cushion of floating‐rate funding that is much less subject to withdrawals. As it turns out, however, the market for such debt is extremely limited. A practical solution, therefore, is to create synthetic long‐term, floating‐rate debt, as illustrated in Figure 13.5. The bank sells long‐term debt in the more traditional, fixed‐rate market, and then receives fixed and pays floating in an IRS. The net result is long‐term floating‐rate debt, as desired.

13.4 COUNTERPARTY CREDIT RISK

Each counterparty to a swap contract bears the risk that the other will default on its obligations. A crucial mitigant of this risk is the safe harbor of swaps agreements from the bankruptcy code. In the event of a default, most creditors cannot immediately act to recover amounts owed to them. For example, a bank with an outstanding commercial loan that is secured by production machinery cannot, upon default, seize the collateral and sell it, and so recover the loan amount. Instead, the bank is subject to a bankruptcy stay. Under bankruptcy protection, the defaulting company is given time to reorganize, during which it may continue to use its machinery. At some point, with the permission of the bankruptcy court, the bank's loan will be paid off or restructured, possibly but not necessarily through the sale of the bank's collateral. Swap agreements, however, under their safe harbor, are not subject to the bankruptcy stay.¹⁰ More specifically, if one counterparty defaults on its obligations under a swap contract, the other counterparty may terminate that contract and any others included in a master agreement with the defaulting counterparty; may net receivables and payables under all contracts included in the master agreement; and may liquidate any posted collateral under the agreement to cover swap closeout costs.

Without the safe harbor, then, the surviving counterparty would have to continue making the payments it owes, while no longer receiving payments from the defaulting counterparty, until a court settled the matter. With the safe harbor, however, the surviving counterparty may terminate contracts and stop making payments. Hence, the exposure to the surviving counterparty in the event of a default is the total NPV across all of the contracts with the defaulting counterparty. Put another way, any net positive NPV the surviving counterparty has against the defaulting counterparty is jeopardized by the default and termination of all trades. Furthermore, under the safe harbor, the surviving counterparty may recover potentially lost NPV by selling any collateral posted by the defaulting counterparty and, to the extent those proceeds are insufficient, may pursue an unsecured claim against the defaulting party through the courts. By the way, after a closeout, the surviving party must pay to settle any net negative NPV it has against the defaulting party. The policy justification behind the derivatives safe harbor is that financial institutions, which are typically highly leveraged, could suffer great losses through a bankruptcy process in which they did not know their risk, because they did not know which of their contracts would ultimately be honored and which would not.¹¹ Since the financial crisis of 2007–2009, the safe harbor has been narrowed somewhat to give a governmental authority time to liquidate a failing, systemically important financial institution before its derivatives contracts are terminated, but that process is not explored further in this chapter.

One way dealers have managed the counterparty credit risk from derivatives customers is by collecting a fee, or insurance premium, sometimes called a credit valuation adjustment (CVA) charge, that incorporates the likelihood of default and the potential exposure of the position. These fees, often imposed on the customer as a higher rate when paying fixed or as a lower rate when receiving fixed, constitute a reserve that can make up for losses from the few defaults that actually occur. This means of managing credit risk is particularly suitable for a diversified group of creditworthy clients that have neither ready sources of cash nor the operational infrastructure to post and monitor collateral.

The predominant way dealers have managed counterparty credit risk, however, particularly when trading with professional investment firms, like asset managers and hedge funds, and with other dealers, is by taking collateral through variation margin (VM) and initial margin (IM).¹² Calls for VM ensure that the counterparty with a positive NPV always holds sufficient collateral to cover a loss of that NPV, which, in this context, is sometimes called the current exposure of the swap. As an example, consider an IRS in which Counterparty A agrees to receive fixed from Counterparty B. At initiation, as discussed earlier, the NPV of a swap is zero. Now say that market interest rates fall such that Counterparty A has a positive NPV of $1 million against Counterparty B. In that case, Counterparty B must post $1 million of collateral to Counterparty A. Subsequently, however, rates rise dramatically, such that the NPV of the swap is positive $2 million to Counterparty B. Counterparty A must then return the $1 million that Counterparty B had posted and send an additional $2 million, so that now Counterparty B holds total net collateral from Counterparty A equal to its positive NPV or current exposure. VM calls are typically made daily, though they can be more frequent in times of heightened market volatility.

The VM arrangement described in the previous paragraph is now called VM collateralized‐to‐market (CTM), because of a recent change in margin arrangements for cleared IRS. For positions against a clearinghouse, IRS VM is now settled‐to‐market (STM), which means that VM flows are not collateral postings, but irrevocable cash settlements of daily profit or loss on the position, just like the daily settlement payments of futures contracts described in Chapter 11. Recasting the example in the previous paragraph under VM STM, after rates fall, Counterparty B pays $1 million outright to Counterparty A. After rates subsequently rise, Counterparty A pays $3 million outright to Counterparty B. At that point, the NPV of the swap to Counterparty B is positive $2 million, but Counterparty B has already collected a net of $2 million from the VM STM payments.¹³

To complete the explanation of how VM protects the counterparty with positive NPV, continue the example by assuming that Counterparty A defaults right after its last VM payment. Under the safe harbor, Counterparty B tears up the swap with Counterparty A and, therefore, no longer receives or makes payments under that contract. Counterparty B needs to replace the contract, however, to restore the economics of the position before the default. Under VM CTM, Counterparty B relies again on the safe harbor to seize the net $2 million of collateral collected from Counterparty A through the VM arrangement, and pays that $2 million to some Counterparty C to enter into a swap at the same terms as the swap just canceled. By the definition of NPV – ignoring transactions costs, which are discussed further presently – Counterparty C is willing to receive fixed at a below‐market rate in a swap with a negative NPV of $2 million in exchange for a payment of $2 million. Lastly, Counterparty C immediately sends that $2 million back to Counterparty B as collateral against its newly acquired negative NPV. To emphasize that it is fair for Counterparty C to enter into this swap, note that, while Counterparty C is receiving a below‐market rate of interest, if rates remain constant, the NPV of the swap to Counterparty C will gradually increase from −$2 million to 0, and Counterparty C will get back $2 million of collateral that it never paid for. Put another way, by entering into this swap, Counterparty C essentially takes a position in a bond with a below‐market coupon at a price of 98. The coupon is below market, but the price will increase to 100 at maturity.

Under VM STM, Counterparty B collected a total of $2 million over time as the NPV of the swap rose to $2 million, but holds no collateral at the time of default. Some Counterparty C again steps into the replacement swap, which receives a below‐market rate and, consequently, has a negative NPV. Under VM STM, however, Counterparty C is responsible only for making payments arising from subsequent changes in NPV. Hence, there is no exchange of cash or collateral when Counterparty C enters into the swap under VM STM. Again, Counterparty C receives a below‐market rate over time, but, on average, settlement payments are positive as the NPV rises from −$2 million to zero.

While VM is sufficient to protect a positive NPV immediately after each VM call, it does not protect changes in NPV between VM calls. Continuing with the example, say that rates rise again so that Counterparty B's NPV increases from $2 million to $3 million, and Counterparty A defaults before meeting its VM call. Counterparty B then has an exposure and possible loss of $1 million. To protect against value changes between VM calls, each counterparty holds a certain amount of IM posted by the other. The amount of IM is typically set so as to cover a large market move plus the transaction and liquidity costs of replacing the defaulting positions. For example, statistical analysis might indicate that, with 99% statistical confidence, the swap between Counterparty A and Counterparty B will move by less than $5 million before it can be replaced, and market expertise might indicate that replacing a swap of its notional amount incurs an additional $250,000 in transaction and market impact costs. The IM for the trade, therefore, might be set at $5,250,000. In this way, so long as the change in NPV between VM calls is less than posted IM, each counterparty has enough collateral to replace defaulted positions. Continuing with the example in a VM CTM arrangement, Counterparty B seizes $1 million of IM collateral, which, together with the VM of $2 million is enough to pay Counterparty C to take on the now negative $3 million NPV position. The remaining $4,250,000 of IM is returned to Counterparty A, the defaulting counterparty. In a VM STM arrangement, Counterparty B seizes $1 million of IM collateral, bringing the total collected to $3 million, which is now the NPV of the swap to Counterparty B. The remaining IM is returned to Counterparty A. Some Counterparty C steps into the swap, facing a negative NPV, but with obligations to make only future VM STM payments.

In general, collateral is posted in cash, in which case it earns some rate of interest, or in safe securities, like government bonds, in which case the counterparty posting the collateral keeps the interest. Securities posted as collateral might be accepted only at a haircut, that is, at less than their market value, so as to reflect the price risk should they have to be liquidated in the event of a default. At a haircut of 3%, for example, $100 of securities count only as $97 against collateral requirements. For cleared trades, the amount of IM to be posted is set and computed by the clearinghouse, and, for non‐cleared trades, either using internal firm models or the industry standard initial margin model (SIMM). An important quantity in the determination of IM is the margin period of risk (MPOR), which is the assumed time interval over which a defaulted swap can be hedged or replaced. After a default, it is usual to hedge the replacement of the defaulted swap first and then – if desired – replace the actual swap with a willing counterparty and unwind the hedge. For example, say that Counterparty A defaults on its obligation to pay Counterparty B fixed at 2.34% on a swap with a remaining maturity of 12.3 years. Because it is likely to take some time to replace that particular swap, Counterparty B should first hedge the exposure it lost on account of the default by receiving fixed on a DV01‐neutral amount of a 10‐year swap at the prevailing market rate. Then, if desired, Counterparty B can find a counterparty to replace the original swap – along the lines previously discussed – and then, when the replacement swap is in place, unwind the hedge. In any case, the longer the MPOR, the greater the assumed possible changes in NPV before hedging or replacement, and the greater the required IM to ensure that sufficient funds are available for hedging and replacing the defaulted swap.

Before the financial crisis of 2007–2009, nearly all IRS were traded over‐the‐counter (OTC) and managed bilaterally. OTC trading means that the parties arrange transactions on their own, without a third‐party platform or exchange. And in bilateral trades, each pair of counterparties sets margin rules, exchanges collateral, and bears the risk of each other's default. While IRS played no appreciable role in the financial crisis,¹⁴ the Dodd‐Frank Act required that all relatively liquid swaps be traded on a swaps execution facility and be cleared. The clearinghouse then sets margin rules and manages collateral, as is described in greater detail in the next section. Dodd‐Frank further required that margin be exchanged by counterparties to any swaps that are not cleared, and that all swaps transactions and positions be reported to regulators through swap data repositories. Dodd‐Frank and its implementing regulations exempt nonfinancial, commercial end users, who are using swaps to hedge, from clearing and margin requirements. This means, for example, that a nonfinancial corporation, which has neither the ability to fund margin calls nor the operational ability to manage the exchange of margin, can use a bilaterally arranged swap to hedge a debt issue, so long as it can find a willing dealer. As an aside, the business models of certain financial entities, like insurance companies and pension funds, are very suited to using IRS, but not to the liquidity demands of margin requirements.¹⁵ These entities, however, unless they are very small, are not exempt from clearing and margin requirements.

The clearing requirement of Dodd‐Frank resulted in the clearing of the vast majority of IRS, which, until recently, were dominated by LIBOR swaps. At the time of this writing, SOFR swaps are relatively new and have not yet been deemed liquid enough for the clearing requirement to apply. Nevertheless, over 70% of SOFR swaps are being cleared anyway, and the clearing requirement is likely to be applied to them in 2022 or soon thereafter.¹⁶

13.5 CLEARING AND CENTRAL COUNTERPARTIES

Figure 13.6 illustrates the difference between bilateral and cleared swaps. The top section of the figure shows a bilateral swap, in which Counterparty A pays fixed to and receives floating from Counterparty B. All aspects of the trade, from its execution to the ongoing exchange of cash flows and margin, are arranged between the two counterparties, and each counterparty bears all of the risk should the other default. While the diagram looks simple when there are only two counterparties, managing a large book of swaps trades with many counterparties is very complex. Every day, each counterparty has to send VM to or collect VM from each of its counterparties, in addition to sending or collecting any contractual interest payments due that day. Furthermore, each counterparty must track its exposure to each of its counterparties and perform ongoing due diligence as to their creditworthiness.

The middle section of Figure 13.6 illustrates a cleared swap between two firms that are members of the clearinghouse. Members 1 and 2 first execute a swap with each other, which is not shown in the figure, in which Member 1 pays fixed to Member 2. That swap is then given up for clearing, which means that it is canceled and replaced with the two swaps shown in the figure: one in which Member 1 pays fixed to the clearinghouse, acting in its capacity as a central counterparty (CCP), and one in which the CCP pays fixed to Member 2. Note that the CCP takes no cash flow risk or market risk: the amounts received from Member 1 are simply passed to Member 2, and the amounts received from Member 2 are simply passed to Member 1. In any case, each member now legally faces the CCP and posts collateral to the CCP. If either member defaults, the CCP manages the default and suffers losses. However, as discussed further presently, large losses might have to be covered by the broader membership. This backstopping of losses by the membership is represented in the figure as the light gray circles surrounding the swap cash flows. On the other hand, if the CCP defaults, Members 1 and 2 have recourse only to the CCP, not to each other.

The bottom section of Figure 13.6 illustrates a cleared swap between a member of the clearinghouse and a client of that member. The original swap between the two (not shown), as before, is transformed into two swaps, each facing the clearinghouse. And, as before, a default by the member is backstopped by the CCP and the broader membership. However, a default by the client, who is sponsored by Member 1 to face the CCP, is backstopped first by Member 1. This backstopping is represented in the figure by the dark gray circle around the cash flows of this swap. But if Member 1 defaults as well, then, as before, losses are backstopped by both the CCP and the broader membership. This fallback is represented in the figure by the light gray circle surrounding the darker one. While this section of the figure illustrates a trade between Member 1 and its client, the logic of this paragraph can be extended to other trading permutations: member trades are backstopped by the CCP and the broader membership, while client trades are backstopped first by the sponsoring member and then by the CCP and the broader membership.

Relative to bilateral trading of IRS, clearing greatly simplifies operations. Regardless of the number of positions and the history of who traded with whom, at the end of each day, each counterparty to the CCP makes only one net payment to or receives one net payment from the CCP. Clearing also greatly simplifies counterparty risk management in that each counterparty need be satisfied only with the creditworthiness of the CCP, although that creditworthiness – while extremely high – can be challenging to evaluate precisely. While clearing confers significant and extensive advantages, these come at some opportunity costs. Clearing nets positions within the same product class, but sacrifices netting across product classes. For example, a dealer who has IRS, repo, and credit default swap positions with one particular client might very well prefer to net the cash flows across those positions in‐house instead of holding the IRS position against one CCP, the repo directly against the client, and the credit default swaps against a different CCP. The legal requirement to clear, however, outlaws this in‐house netting option. Clearing also outsources margin methodologies and default management to the CCP, which, while advantageous to smaller counterparties, might not be optimal for those with broader operations.

Risk management at a CCP subsumes many functions. First, the CCP must set criteria for admitting members and monitoring their creditworthiness over time. Second, the CCP must set margin requirements. As discussed already, the amount of VM calls is conceptually straightforward, as they reflect changes in NPV. The appropriate amounts of IM, however, depend on complex analyses of market volatility and liquidity conditions. Third, the CCP must establish procedures for default management and execute them well as defaults occur. When a client of a member defaults, the sponsoring member is responsible, and when a member defaults, the CCP is responsible. More specifically, the CCP must make VM STM payments to the non‐defaulting sides of the swap and replace the defaulting swaps along the lines described earlier. Note that, while a dealer may decide to replace lost exposure with similar exposure, the business model of the CCP is not to take any market risk at all. The swap lost must ultimately be replaced with a swap of exactly the same terms. In any case, the CCP's first source of funds is the IM posted by the defaulting member, along the aforementioned lines. If that proves insufficient, however, the CCP gathers the necessary funds according to a prespecified default waterfall.

Figure 13.7 illustrates a waterfall but is not drawn to the scale of the underlying resources. The first resource, just discussed, is the IM posted by the defaulting member. In addition to posting IM, however, members have to contribute to a default fund or guarantee fund, in proportion to the size of their positions against the CCP. One rule of thumb is that the total default fund should be large enough to withstand the simultaneous default of the two members with the largest positions. In any case, if the defaulter's IM is not sufficient to cover the CCP's losses, the defaulter's default fund contribution is tapped.¹⁷ If that is insufficient as well, capital contributed by the CCP is tapped. Relative to the size of the total of all members default fund contributions, CCP capital is typically quite small. This buffer is sometimes referred to as the CCP skin‐in‐the‐game, and its size is the subject of much debate. To oversimplify that debate, CCPs argue that, because almost all of the risk comes from member positions, almost all of the waterfall protections should come from members. Members, on the other hand, argue that, because CCPs manage risk with the profits of their shareholders as an important consideration, they should contribute a significant buffer as well. In any case, if CCP capital is exhausted with losses still needing to be covered, the default fund from the surviving members is tapped. The waterfall to this point explains the sense in which the membership as a whole backstops member contracts. It is also the sense in which CCPs mutualize losses. Loose descriptions of clearing say that CCPs “eliminate” counterparty credit risk, but that is not accurate. When a swap is cleared, its counterparty credit risk moves from the original counterparty to the CCP and its membership as a whole.

With VM covering daily market moves, IM covering all but the largest of market moves between VM calls, and the default fund sized to withstand the default of the two members with the largest positions – who are almost certainly large and heavily regulated financial institutions themselves – only a record‐breaking financial tsunami could generate losses that require stepping further down the waterfall. The next sources of funds, however, are as follows. Members agree to comply with certain assessments or call for funds should the waterfall get to this point. These assessments are called unfunded, because the CCP does not hold them in reserve, as it does IM and default fund contributions. While legally binding, there is always some concern that, in a crisis, assessments might not be honored promptly and in full. If assessments are insufficient to cover losses, then some fraction of VM owed to market participants would not be paid, in a process known as VM haircutting. After that, the sources of last recourse include voluntary contributions and other actions taken by members. If that proves insufficient, CCP ceases operations.

This section concludes with a brief mention of three topical public policy issues. First, the shift to clearing the vast majority of IRS may or may not have significantly reduced systemic risk relative to various alternatives, but it has certainly concentrated that risk. Nearly all GBP‐denominated IRS are cleared at the London Clearing House (LCH); the vast majority of USD‐denominated IRS are cleared at LCH as well, with the Chicago Mercantile Exchange (CME) a distant second; the vast majority of EUR‐denominated swaps are cleared at LCH, with the exception of the smaller but growing segment of €STR swaps, in which Eurex has a growing market share; and clearing of JPY‐denominated swaps is shared between LCH and the Japanese Securities Clearing Corporation (JSCC).¹⁸ From a systemic risk perspective, legislators and regulators seem to have followed the advice of Andrew Carnegie: “put all your eggs in one basket and then watch that basket.”

A second policy issue pertains to CCP margin. Margin, along with other risk management practices of a CCP, are designed to make it extremely unlikely that any counterparty loses money from counterparty risk. Part of this outcome, however, is due to the ability of CCPs to set IM and also to raise required IM when market volatility or financial stress increases. In this sense then, reducing counterparty risk increases liquidity risk. Many are concerned with how increasing IM might exacerbate financial stress, known as margin procyclicality, but there are no easy solutions. Raising margin in a crisis is an important risk management tool at a CCP but might make it challenging for members and other market participants both to meet their increasing obligations to the CCP and to continue meeting their non‐derivatives obligations.

The third policy issue relates to CCP governance. Before clearing was required, market participants could consider clearing as one of several choices and could decide to clear or not to clear. With required clearing and the concentration of clearing in very few CCPs, market participants, including members, have much less leverage with respect to CCP risk management and other practices. The resolution of this issue is also far from straightforward.

13.6 BASIS SWAPS

Both OIS and fixed‐for‐floating swaps pay interest at a fixed rate on one leg and at a floating rate on the other leg. A basis swap, by contrast pays interest at one floating rate on one leg and interest on a different floating rate on another leg. Before the transition away from LIBOR, basis swap volumes were particularly large in exchanging LIBOR of one term against LIBOR of another term, and swaps of effective fed funds (see Chapter 12) against LIBOR of various terms were common as well. In US dollar markets, swaps of SOFR against LIBOR are trading actively in the transition period but will fade with the disappearance of LIBOR. Cross‐currency basis swaps have been and continue to be extremely popular. These swaps exchange interest at a short‐term rate in one currency for interest at a short‐term rate in another currency, for example, SOFR versus €STR. This section focuses on basis swaps of €STR versus three‐month Euribor to explain concepts, both because Euribor is still an active rate and because foreign exchange rates are outside the scope of this edition of the book.

Consider a bank that funds itself at €STR flat (i.e., without a spread) and lends money to customers at three‐month Euribor plus 1%. This bank has the basis risk that €STR, compounded over a relevant time period, rises relative to three‐month Euribor, compounded over that same period. In general, by the way, the term “basis risk” refers to the risk that two rates or prices, which usually change together in some fixed or predictable relationship, diverge in an unusual and unfavorable way. In any case, Figure 13.8 shows how the bank can hedge its basis risk with an €STR versus three‐month Euribor basis swap. As of February 2022, the two‐year €STR versus three‐month Euribor basis swap spread was 13.8 basis points, which means that the bank, as shown in the figure, can receive €STR plus 13.8 basis points and pay three‐month Euribor on some notional amount for two years. More specifically, at the end of every quarter during those two years, the bank receives interest at daily compounded €STR plus 13.8 basis points over that quarter (along the lines of Figure 13.1), and the bank pays interest at three‐month Euribor set at the start of the quarter (along the lines of Figure 13.2). Overall then, with its basis swap hedge, the bank in Figure 13.8 locks in a fixed rate of 1.138%, so long as its customers do not default. Put another way, the customers pay a credit and liquidity spread of 1.138% over the near‐riskless €STR: 1% as a spread over three‐month Euribor and 13.8 basis points as a spread of three‐month Euribor over €STR.

From the swap dealer's perspective, there is virtually no credit risk: the bank itself is probably a good credit and the basis swap is collateralized. Because Euribor is a riskier rate than €STR, however, compounded €STR over a quarter will normally be less than three‐month Euribor. It makes sense, therefore, that paying a spread over €STR is fair against receiving three‐month Euribor, although the market determination of the exact spread can certainly be the subject of further analysis.

The existence of basis swap spreads shows that not all swaps can be valued using the methodology for pricing swaps that is given in Chapter 2 and earlier in this chapter. That methodology argued that the floating leg (including the fictional notional amount) is worth par when the floating rate is considered to be the risk‐free rate, that is, the rate at which funds can be moved without risk across time. And it is reasonable to classify both overnight SOFR and overnight €STR as risk‐free rates.¹⁹ The same is not true, however, for three‐month Euribor. Or, to put it another way, it cannot be simultaneously true that i) a floating leg paying €STR is worth par; ii) €STR plus 13.8 basis point is fair against three‐month Euribor for two years; and iii) a floating leg paying three‐month Euribor for two years is worth par.

The appropriate methodology for valuing a fixed‐for‐floating swap when the floating index is not a risk‐free rate, like Euribor, is the following. First, discount the fixed cash flows (including the fictional notional amount) at the discount factors implied by swaps against the risk‐free rate index, like €STR. These calculations are described in Chapter 2. Second, the value of the floating leg is equal to par plus the present value of payments of the basis swap spread, where discounting is again done using the risk‐free rates. For example, the basis swap in Figure 13.8 shows that the value of receiving three‐month Euribor equals the value of receiving €STR plus 13.8 basis points. But the value of receiving €STR (including the fictional notional amount) is par. Therefore, the value of receiving three‐month Euribor quarterly for two years is par plus the present value of receiving 13.8 basis points, paid quarterly, for two years.

Appendix A13.1 illustrates the calculations outlined in the previous paragraph with representative market rates toward the end of February 2022, when the fixed rate on a two‐year, fixed versus three‐month Euribor swap was 0.078% and, as already mentioned, the two‐year €STR versus three‐month Euribor basis swap spread was 13.8 basis points. The values of both the fixed and floating sides are calculated to be 100.281. To summarize, when the floating index is a risk‐free rate, both sides of a fixed‐for‐floating swap at initiation are worth par. When the floating index is not a risk‐free rate, but trades with a positive basis swap spread against the risk‐free rate, both sides of the swap at initiation are equal in value, of course, but each side is worth more than par. Note that traders may just accept that rates on newly initiated swaps are fair and, therefore, may not care about the value of each side separately. Nevertheless, a methodology is required to compute the NPVs of existing swaps in a trading book, which are not observable in the market.

The pricing methodology just described can take rates on €STR swaps and spreads on €STR versus three‐month Euribor basis swaps as given to price fixed versus three‐month Euribor swaps. Alternatively, the methodology can take rates on €STR swaps and on fixed versus three‐month Euribor swaps as given to imply fair basis swap spreads. The latter approach, called two‐curve pricing, is often preferred when basis swaps of all terms are insufficiently liquid. In fact, two‐curve pricing typically does not explicitly calculate basis swap spreads at all. A brief description of this methodology is given in Appendix A13.2.