on March 1, 2003, it will pay $30,000and receive 100S, where S is the market price of one ounce of gold on that date.
Whereas a forward contract leads to the exchange of cash flows on just one future date, swapstypically lead to cash flow exchanges taking place on several future dates. The first swap contractswere negotiated in the early 1980s. Since then the market has seen phenomenal growth. In thischapter we examine how swaps are designed, how they are used, and how they can be valued. Ourdiscussion centers on the two popular types of swaps: plain vanilla interest rate swaps and fixed-for-fixed currency swaps. Other types of swaps are discussed in Chapter 25.
61 ACCLIAwaa evan
 
 
The most common type of swap is a “plain vanilla” interest rate swap. In this, a company agrees topay cash flows equal to interest at a predetermined fixed rate on a notional principal for a numberof years. In return, it receives interest at a floating rate on the same notional principal for the sameperiod of time.
The floating rate in many interest rate swap agreements is the London Interbank Offer Rate(LIBOR). This was introduced in Chapter 5. LIBOR is the rate of interest offered by banks ondeposits from other banks in Eurocurrency markets. One-month LIBOR is the rate offered on one-month deposits, three-month LIBOR is the rate offered on three-month deposits, and so on.LIBOR rates are determined by trading between banks and change frequently so that the supply offunds in the interbank market equals the demand for funds in that market. Just as prime is oftenthe reference rate of interest for floating-rate loans in the domestic financial market, LIBOR is areference rate of interest for loans in international financial markets. To understand how it is used,consider a five-year loan with a rate of interest specified as six-month LIBOR plus 0.5% perannum. The life of the loan is divided into ten periods, each six months in length. For each periodthe rate of interest is set at 0.5% per annum above the six-month LIBOR rate at the beginning ofthe period. Interest is paid at the end of the period.
125126 CIIAPTER 6
MMustration
Consider a hypothetical three-year swap initiated on March 5, 2003, between Microsoft and Intel.We suppose Microsoft agrees to pay to Intel an interest rate of 5% per annum on a notionalprincipal of $100 million, and in return Intel agrees to pay Microsoft the six-month LIBOR rate onthe same notional principal. We assume the agreement specifies that payments are to be exchangedevery six months, and the 5% interest rate is quoted with semiannual compounding. This swap isrepresented diagrammatically in Figure 6.1.
The first exchange of payments would take place on September 5, 2003, six months after theinitiation of the agreement. Microsoft would pay Intel $2.5 million. This is the interest on the $100million principal for six months at 5%. Intel would pay Microsoft interest on the $100 millionprincipal at the six-month LIBOR rate prevailing six months prior to September 5, 2003— that is, onMarch 5, 2003. Suppose that the six-month LIBOR rate on March 5, 2003, is 4.2%. Intel pays Micro-soft 0.5 x 0.042 x $100 = $2.1 million.’ Note that there is no uncertainty about this first exchangeof payments because it is determined by the LIBOR rate at the time the contract is entered into.
The second exchange of payments would take place on March 5, 2004, one year after theinitiation of the agreement. Microsoft would pay $2.5 million to Intel. Intel would pay interest onthe $100 million principal to Microsoft at the six-month LIBOR rate prevailing six months prior toMarch 5, 2004— that is, on September 5, 2003. Suppose that the six-month LIBOR rate onSeptember 5, 2003, is 4.8%. Intel pays 0.5 x 0.048 x $100 = $2.4 million to Microsoft.
In total, there are six exchanges of payment on the swap. The fixed payments are always $2.5million. The floating-rate payments on a payment date are calculated using the six-month LIBORrate prevailing six months before the payment date. An interest rate swap is generally structured sothat one side remits the difference between the two payments to the other side. In our example,Microsoft would pay Intel $0.4 million (= $2.5 million — $2.1 million) on September 5, 2003, and$0.1 million (= $2.5 million — $2.4 million) on March 5, 2004.
Table 6.1 provides a complete example of the payments made under the swap for one particularset of six-month ITBOR rates. The table shows the swap cash flows from the perspective ofMicrosoft. Note that the $100 million principal is used only for the calculation of interestpayments. The principal itself is not exchanged. This is why it is termed the notional principal.
If the principal were exchanged at the end of the life of the swap, the nature of the deal wouldnot be changed in any way. The principal is the same for both the fixed and floating payments.Exchanging $100 million for $100 million at the end of the life of the swap is a transaction thatwould have no financial value to either Microsoft or Intel. Table 6.2 shows the cash flows inTable 6.1 with a final exchange of principal added in. This provides an interesting way of viewingthe swap. The cash flows in the third column of this table are the cash flows from a long position ina floating-rate bond. The cash flows in the fourth column of the table are the cash flows from ashort position in a fixed-rate bond. The table shows that the swap can be regarded as the exchange
 
 
5.0%—_—__—_____
Intel MicrosoftLIBOR
 
 
 
 
 
 
Figure 6.1 Interest rate swap between Microsoft and Intel
' The calculations here are slightly inaccurate because they ignore day count conventions. This point is discussed inmore detail later in the chapter.Swaps 127
Table 6.1. Cash flows (millions of dollars) to Microsoft in a $100 million three-year interestrate swap when a fixed rate of 5% is paid and LIBOR is received
 
6-month LIBOR Floating cash flow Fixed cash flow Net
Date rate (%) received paid cash flowMarch 5, 2003 4.20
September 5, 2003 4.80 +2.10 —2.50 —0.40March 5, 2004 5.30 +2.40 —2.50 —0.10September 5, 2004 5.50 +2.65 —2.50 +0.15March 5, 2005 5.60 +2.75 —2.50 +0.25September 5, 2005 5.90 +2.80 —2.50 +0.30
 
March 5, 2006 6.40 +2.95 —2.50 +0.45
of a fixed-rate bond for a floating-rate bond. Microsoft, whose position is described by Table 6.2, islong a floating-rate bond and short a fixed-rate bond. Intel is long a fixed-rate bond and short afloating-rate bond.
This characterization of the cash flows in the swap helps to explain why the floating rate in theswap is set six months before it is paid. On a floating-rate bond, interest is usually set at the beginningof the period to which it will apply and is paid at the end of the period. The calculation of thefloating-rate payments in a “plain vanilla” interest rate swap, such as that in Table 6.2, reflects this.
Using the Swap to Transform a Liability
For Microsoft, the swap could be used to transform a floating-rate loan into a fixed-rate loan.Suppose that Microsoft has arranged to borrow $100 million at LIBOR plus 10 basis points. (Onebasis point is one-hundredth of 1%, so the rate is LIBOR plus 0.1%.) After Microsoft has enteredinto the swap, it has three sets of cash flows:
L. It pays LIBOR plus 0.1% to its outside lenders.
2. It receives LIBOR under the terms of the swap.
3. It pays 5% under the terms of the swap.
Table 6.2 Cash flows (millions of dollars) from Table 6.1 when there is a final exchangeof principal
 
6-month LIBOR Floating cash flow __ Fixed cash flow Net
Date rate (%) received paid cash flowMarch 5, 2003 4.20
September 5, 2003 4.80 +2.10 —2.50 —0.40March 5, 2004 5.30 +2.40 ~2.50 —0.10September 5, 2004 5.50 +2.65 —2.50 +0.15March 5, 2005 5.60 +2.75 —2.50 +0.25September 5, 2005 5.90 +2.80 —2.50 +0.30
 
 
March 5, 2006 6.40 +102.95 —102.50 +0.45128 CHAPTER 6
5.2%Microsoft
Figure 6.2 Microsoft and Intel use the swap to transform a liability
  
LIBOR + 0.1%
 
These three sets of cash flows net out to an interest rate payment of 5.1%. Thus, for Microsoft, theswap could have the effect of transforming borrowings at a floating rate of LIBOR plus 10 basispoints into borrowings at a fixed rate of 5.1%.
For Intel, the swap could have the effect of transforming a fixed-rate loan into a floating-rateloan. Suppose that Intel has a three-year $100 million loan outstanding on which it pays 5.2%.After it has entered into the swap, it has three sets of cash flows:
lL. It pays 5.2% to its outside lenders.2. It pays LIBOR under the terms of the swap.3. It receives 5% under the terms of the swap.
These three sets of cash flows net out to an interest rate payment of LIBOR plus 0.2% (or LIBORplus 20 basis points). Thus, for Intel, the swap could have the effect of transforming borrowings ata fixed rate of 5.2% into borrowings at a floating rate of LIBOR plus 20 basis points. Thesepotential uses of the swap by Intel and Microsoft are illustrated in Figure 6.2.
Using the Swap to Transform an Asset
Swaps can also be used to transform the nature of an asset. Consider Microsoft in our example.The swap could have the effect of transforming an asset earning a fixed rate of interest into an assetearning a floating rate of interest. Suppose that Microsoft owns $100 million in bonds that willprovide interest at 4.7% per annum over the next three years. After Microsoft has entered into theswap, it has three sets of cash flows:
1, Ht receives 4.7% on the bonds.
2. It receives LIBOR under the terms of the swap.3. It pays 5% under the terms of the swap.
These three sets of cash flows net out to an interest rate inflow of LIBOR minus 30 basis points.Thus, one possible use of the swap for Microsoft is to transform an asset earning 4.7% into anasset earning LIBOR minus 30 basis points.
Now consider Intel. The swap could have the effect of transforming an asset earning a floatingrate of interest into an asset earning a fixed rate of interest. Suppose that Intel has an investment of
AT%
   
Microsoft
 
LIBOR - 0.25%
Figure 6.3 Microsoft and Intel use the swap to transform an assetSwaps 129
 
 
     
  
4.985% 5.015%
LC Microsoft
5.2%~— Intel
   
Financialinstitution
     
 
 
 
-———_—>]LIBOR LIBOR + 0.1%
 
Figure 6.4 Interest rate swap from Figure 6.2 when a financial institution is used
$100 million that yields LIBOR minus 25 basis points. After it has entered into the swap, it hasthree sets of cash flows:
L. It receives LIBOR minus 25 basis points on its investment.2. It pays LIBOR under the terms of the swap.
3. It receives 5% under the terms of the swap.
These three sets of cash flows net out to an interest rate inflow of 4.75%. Thus, one possible useof the swap for Intel is to transform an asset earning LIBOR minus 25 basis points into an asset
earning 4.75%. These potential uses of the swap by Intel and Microsoft are illustrated inFigure 6.3.
gure
Role of Financial Intermediary
Usually two nonfinancial companies such as Intel and Microsoft do not get in touch directly toarrange a swap in the way indicated in Figures 6.2 and 6.3. They each deal with a financialintermediary such as a bank or other financial institution. “Plain vanilla” fixed-for-floating swapson U.S. interest rates are usually structured so that the financial institution earns about 3 or 4 basispoints (0.03 to 0.04%) on a pair of offsetting transactions.
Figure 6.4 shows what the role of the financial institution might be in the situation in Figure 6.2.The financial institution enters into two offsetting swap transactions with Intel and Microsoft.Assuming that neither defaults, the financial institution is certain to make a profit of 0.03% (3 basispoints) per year multiplied by the notional principal of $100 million. (This amounts to $30,000 peryear for the three-year period.) Microsoft ends up borrowing at 5.115% (instead of 5.1%, as inFigure 6.2). Intel ends up borrowing at LIBOR plus 21.5 basis points (instead of at LIBOR plus20 basis points, as in Figure 6.2).
Figure 6.5 illustrates the role of the financial institution in the situation in Figure 6.3. Again,the financial institution is certain to make a profit of 3 basis points if neither company defaultson the swap. Microsoft ends up earning LIBOR minus 31.5 basis points (instead of LIBORminus 30 basis points, as in Figure 6.3). Intel ends up earning 4.735% (instead of 4.75%, as inFigure 6.3).
Note that in each case the financial institution has two separate contracts: one with Intel andthe other with Microsoft. In most instances, Intel will not even know that the financial institution
4.985% 5.015%
       
         
 
Financial 4.7%
Intel institution
LIBOR — 0.25%
 
 
Figure 6.5 Interest rate swap from Figure 6.3 when a financial institution is used130 CHAPTER 6
has entered into an offsetting swap with Microsoft, and vice versa. If one of the companiesdefaults, the financial institution still has to honor its agreement with the other company. The3-basis-point spread earned by the financial institution is partly to compensate it for the defaultrisk it is bearing.
Market Makers
In practice, it is unlikely that two companies will contact a financial institution at the same timeand want to take opposite positions in exactly the same swap. For this reason, many largefinancial institutions act as market makers for swaps. This means that they are prepared to enterinto a swap without having an offsetting swap with another counterparty. Market makers mustcarefully quantify and hedge the risks they are taking. Bonds, forward rate agreements, andinterest rate futures are examples of the instruments that can be used for hedging by swap marketmakers. The way market makers provide quotes in the swap market is discussed later in thischapter.
Day Count Conventions
The day count
ane Gay coun
numbers calculated in the example we have given do not exactly reflect these day count conven-tions. Consider, for example, the six-month LIBOR payments in Table 6.1. Because it is a moneymarket rate, six-month LIBOR is generally quoted on an actual/360 basis. The first floatingpayment in Table 6.1, based on the LIBOR rate of 4.2%, is shown as $2.10 million. Becausethere are 184 days between March 5, 2001, and September 5, 2001, it should be
», 184
* 360
conventions discussed in Section 5.8 affect payments on a swap and some of theconventions ciscussec in section 3.6 alect payments on a swap, anc some ot the
>>
¢x2
= $2.1467 miIn general, a LIBOR-based floating-rate cash flow on a swap payment date is calculated asLRn/360, where L is the principal, R is the relevant LIBOR rate, and n is the number of dayssince the last payment date.
The fixed rate that is paid in a swap transaction is similarly quoted with a particular day countbasis being specified. As a result, the fixed payments may not be exactly equal on each paymentdate. The fixed rate is usually quoted as actual/365 or 30/360. It is not therefore directlycomparable with LIBOR because it applies to a full year. To make the rates comparable, eitherthe six-month LIBOR rate must be multiplied by 365/360 or the fixed rate must be multipliedby 360/365.
For ease of exposition we will ignore day count issues in the examples in the rest of this chapter.
Confirmations
A confirmation is the legal agreement underlying a swap and is signed by representatives of the twoparties. Table 6.3 could be an extract from the confirmation between Microsoft and Intel. Thedrafting of confirmations has been facilitated by the work of the International Swaps andDerivatives Association (ISDA) in New York. This organization has produced a number ofMaster Agreements that consist of clauses defining in some detail the terminology used in swapagreements, what happens in the event of default by either side, and so on. Almost certainly, thefull confirmation for the swap in Table 6.3 would state that the provisions of an ISDA MasterAgreement apply to the contract.Swaps 131
Table6.3 Extract from confirmation for a hypothetical plain vanilla swapbetween Microsoft and Intel
 
Trade date 27-February-2003Effective date 5-March-2003
Business day convention (all dates) Following business dayHoliday calendar US.
Termination date 5-March-2006
Fixed Amounts
Fixed-rate payer Microsoft
Fixed-rate notional principal USD 100 million
Fixed rate 5% per annumFixed-raie day count convention Actuai/365
Fixed rate payment dates Each 5-March and 5-September
commencing 5-September-2003,up to and including 5-March-2006
Floating Amounts
Floating-rate payer Intel
Floating-rate notional principal USD 100 million
Floating rate USD 6-month LIBORFloating-rate day count convention Actual/360
Floating-rate payment dates Each 5-March and 5-September
commencing 5-September-2003,up to and including 5-March-2006
 
Table 6.3 specifies that the following business day convention is to be used and that the U.S.calendar determines which days are business days and which days are holidays. This means that, ifa payment date falls on a weekend or a U.S. holiday, the payment is made on the next businessday.’ In the example in Table 6.3, September 5, 2004, is a Sunday. The payment is therefore madeon Monday September 6, 2004.
6.2 THE COMPARATIVE-ADVANTAGE ARGUMENT
 
 
 
An explanation commonly put forward to explain the popularity of swaps concerns comparativeadvantages. Consider the use of an interest rate swap to transform a liability. Some companies, it isargued, have a comparative advantage when borrowing in fixed-rate markets, whereas othercompanies have a comparative advantage in floating-rate markets. To obtain a new loan, it makessense for a company to go to the market where it has a comparative advantage. As a result, thecompany may borrow fixed when it wants floating, or borrow floating when it wants fixed. Theswap is used to transform a fixed-rate loan into a floating-rate loan, and vice versa.
> Another business day convention that is sometimes specified is the modified following business day convention,which is the same as the following business day convention except that when the next business day falls in a differentmonth from the specified day, the payment is made on the immediately preceding business day. Preceding andmodified preceding business day conventions are defined analogously.132 CHAPTER 6
 
Table 6.4 Borrowing rates that provide a basis for thecomparative-advantage argument
 
Fixed FloatingAAACorp 10.0% 6-month LIBOR + 0.3%BRBCaorp 11.2% 6-month TIBOR + 1.0%
Ifustration
Suppose that two companies, AAACorp and BBBCorp, both wish to borrow $10 million for fiveyears and have been offered the rates shown in Table 6.4. AAACorp has a AAA credit rating;BBBCorp has a BBB credit rating. We assume that BBBCorp wants to borrow at a fixed rate ofinterest, whereas AAACorp wants to borrow at a floating rate of interest linked to six-monthLIBOR. BBBCorp, because it has a worse credit rating than AAACorp, pays a higher rate ofinterest than AAACorp in both fixed and floating markets.
A key feature of the rates offered to AAACorp and BBBCorp is that the difference between the twofixed rates is greater than the difference between the two floating rates. BBBCorp pays 1.2% morethan AAACorp in fixed-rate markets and only 0.7% more than AAACorp in floating-rate markets.BBBCorp appears to have a comparative advantage in floating-rate markets, whereas AAACorpappears to have a comparative advantage in fixed-rate markets.? It is this apparent anomaly that canlead to a swap being negotiated. AAACorp borrows fixed-rate funds at 10% per annum. BBBCorpborrows floating-rate funds at LIBOR plus 1% per annum. They then enter into a swap agreement toensure that AAACorp ends up with floating-rate funds and BBBCorp ends up with fixed-rate funds.
To understand how the swap might work, we first assume that AAACorp and BBBCoprp get intouch with each other directly. The sort of swap they might negotiate is shown in Figure 6.6. This isvery similar to our example in Figure 6.2. AAACorp agrees to pay BBBCorp interest at six-monthLIBOR on $10 million. Tn return, BBBCorp agrees to pay AAACorp interest at a fixed rate of9.95% per annum on $10 million.
AAACorp has three sets of interest rate cash flows:
L. It pays 10% per annum to outside lenders.2. It receives 9.95% per annum from BBBCorp.3. It pays LIBOR to BBBCorp.
The net effect of the three cash flows is that AAACorp pays LIBOR plus 0.05% per annum. This is0.25% per annum less than it would pay if it went directly to floating-rate markets. BBBCorp also
 
BBBC
Figure 6.6 Swap agreement between AAACorp and BBBCorp when rates in Table 6.4 apply
3 Note that BBBCorp’s comparative advantage in floating-rate markets does not imply that BBBCorp pays less thanAAACorp in this market. It means that the extra amount that BBBCorp pays over the amount paid by AAACorp isless in this market. One of my students summarized the situation as follows: ‘AAACorp pays more less in fixed-ratemarkets; BBBCorp pays less more in floating-rate markets.”Swaps 133
 
          
9,93% 9.97%
Financial
institution
      
LIBOR + 1%
Figure 6.7 Swap agreement between AAACorp and BBBCorp when rates in Table 6.4 apply and afinancial intermediary is involved
has three sets of interest rate cash flows:
1. It pays LIBOR + 1.0% per annum to outside lenders.2. It receives LIBOR from AAACorp.3. It pays 9.95% per annum to AAACorp.
The net effect of the three cash flows is that BBBCorp pays 10.95% per annum. This is 0.25% perannum less than it would pay if it went directly to fixed-rate markets.
The swap arrangement appears to improve the position of both AAACorp and BBBCorp by0.25% per annum. The total gain is therefore 0.5% per annum. It can be shown that the totalapparent gain from this type of interest rate swap arrangement is always a — b, where a is thedifference between the interest rates facing the two companies in fixed-rate markets, and 6 is thedifference between the interest rates facing the two companies in floating-rate markets. In this case,a=1.2% and b = 0.70%.
If AAACorp and BBBCorp did not deal directly with each other and used a financial institution,an arrangement such as that shown in Figure 6.7 might result. (This is very similar to the examplein Figure 6.4.) In this case, AAACorp ends up borrowing at LIBOR + 0.07%, BBBCorp ends upborrowing at 10.97%, and the financial institution earns a spread of 4 basis points per year. Thegain to AAACorp is 0.23%; the gain to BBBCorp is 0.23%; and the gain to the financialinstitution is 0.04%. The total gain to all three parties is 0.50% as before.
Criticism of the Comparative-Advantage Argument
The comparative-advantage argument we have just outlined for explaining the attractiveness ofinterest rate swaps is open to question. Why, in Table 6.4, should the spreads between the ratesoffered to AAACorp and BBBCorp be different in fixed and floating markets? Now that the swapmarket has been in existence for some time, we might reasonably expect these types of differencesto have been arbitraged away.
The reason that spread differentials appear to exist is due to the nature of the contracts availableto companies in fixed and floating markets. The 10.0% and 11.2% rates available to AAACorpand BBBCorp in fixed-rate markets are five-year rates (e.g., the rates at which the companies canissue five-year fixed-rate bonds). The LIBOR+0.3% and LIBOR +1.0% rates available to
AAACors and BBBCors in floating-rate markets are six-month rates. In the floating-rate marketAAACOTP ana woe LOrp in noating-rate Markets are Six-MONtn rates. in tne noating-rate Marxet,
the lender usually has the opportunity to review the floating rates every six months. If thecreditworthiness of AAACorp or BBBCorp has declined, the lender has the option of increasingthe spread over LIBOR that is charged. In extreme circumstances, the lender can refuse to roll overthe loan at all. The providers of fixed-rate financing do not have the option to change the terms ofthe loan in this way.*
4 If the floating rate loans are structured so that the spread over LIBOR is guaranteed in advance regardless ofchanges in credit rating, there is in practice little or no comparative advantage.134 “CHAPTER 6
 
The spreads between the rates offered to AAACorp and BBBCorp are a reflection of the extentto which BBBCorp is more likely to default than AAACorp. During the next six months, there isvery little chance that either AAACorp or BBBCorp will default. As we look further ahead, defaultstatistics (see, for example, Table 26.6) show that the probability of a default by a company with arelatively low credit rating (such as BBBCorp) increases faster than the probability of a default byacompany with a relatively high credit rating (such as AAACorp). This is why the spread betweenthe five-year rates is greater than the spread between the six-month rates.
After negotiating a floating-rate loan at LIBOR + 1.0% and entering into the swap shown inFigure 6.7, BBBCorp appears to obtain a fixed-rate loan at 10.97%. The arguments just presentedshow that this is not really the case. In practice, the rate paid is 10.97% only if BBBCorp cancontinue to borrow floating-rate funds at a spread of 1.0% over LIBOR. If, for example, the creditrating of BBBCorp declines so that the floating-rate loan is rolled over at LIBOR + 2.0%, the ratepaid by BBBCorp increases to 11.97%. Because BBBCorp’s spread over six-month LIBOR is morelikely to rise than to fall, BBBCorp’s expected average borrowing rate when it enters into the swapis greater than 10.97%.
The swap in Figure 6.7 locks in LIBOR + 0.07% for AAACorp for the whole of the next fiveyears, not just for the next six months. This appears to be a good deal for AAACorp. Thedownside is that it is bearing the risk of a default by the financial institution. If it borrowedfloating-rate funds in the usual way, it would not be bearing this risk.
6.3 SWAP QUOTES AND LIBOR ZERO RATES
 
 
We now return to the interest rate swap in Figure 6.1. We showed in Table 6.2 that it can becharacterized as the difference between two bonds. Although the principal is not exchanged, wecan assume without changing the value of the swap that, at the end of the agreement, Intel pays
Microsoft the notional principal of $100 million and Microsoft pays Intel the same notional
Miucrosolt the notion neipat of OO miuhon Microsolt pays fhe same noho
principal. The swap is then the same as an arrangement in which:
1. Microsoft has lent Intel $100 million at the six-month LIBOR rate.2. Intel has lent Microsoft $100 million at a fixed rate of 5% per annum.
To put it another way, Microsoft has purchased a $100 million floating-rate (LIBOR) bond fromIntel and has sold a $100 million fixed-rate (5% per annum) bond to Intel. The value of the swapto Microsoft is therefore the difference between the values of two bonds. Define:
fix: Value of fixed-rate bond underlying the swapBg: Value of floating-rate bond underlying the swap
The value of the swap to a company receiving floating and paying fixed (Microsoft in our example) is
Vowap = Ba — Bex (6.1)
Swap Rates
Many large financial institutions are market makers in the swap market. This means that they areprepared to quote, for a number of different maturities and a number of different currencies, a bidand an offer for the fixed rate they will exchange for floating. The bid is the fixed rate in a contractSwaps 135
Table 6.5 Bid and offer fixed rates in the swap market and swap rates(percent per annum); payments exchanged semiannually
Maturity Bid Offer Swap rate
 
(years) (%) (%) (4)2 6.03 6.06 6.045
3 6.21 6.24 6.225
4 6.35 6.39 6.370
5