Title: Swaps Chapter 6
1SwapsChapter 6
2SWAPS Swaps are a form of derivative instruments.
Out of the variety of assets underlying swaps we
will cover INTEREST RATES SWAPS, CURRENCY
SWAPS, COMMODITY SWAPS, EQUITY SWAPS and BASIS
SWAPS.
3SWAPSA SWAP is a contract between two parties
for an exchange of cash flows during some time
period. The cash flows are determined based on
the UNDERLYING ASSET
4It follows that a swap involves 1. Two
parties 2. An underlying asset 3. Cash
flows 4. A payment schedule 5. An agreement as
to how to resolve problems
5 1. Two parties
 The two parties in a swap are labeled as party
and counterparty.  They may arrange the swap directly or indirectly.
 In the latter case, there are two swaps, each
between one of the parties and the swap dealer.
62. The Underlying asset is the basis for the
determination of the cash flows. It is almost
never exchanged by the parties.
Examples USD100,000,000, GBP50,000,000, 50,000
barrels of crude oil An equity index
72. The Underlying asset is called the NOTIONAL
AMOUNT Or The PRINCIPAL Because it only serves
to determine the cash flows. Neither party needs
to own it and it almost never changes hands.
83. The cash flows may be of two types a fixed
or a floating cash flow. Fixed interest rate
vs. Floating interest rate Fixed price
Vs. Market price
93. The cash flows The interest rates, fixed or
floating, multiply the notional amount in order
to determine the cash flows. Ex (10M)(.07)700,
000 Fixed. (10M)(Lt30bps) Floating. The
price, fixed or market, multiply the commodity
notional amount in order to determine the cash
flows. If the underlying asset are 100,000
barrels of oil Ex (100,000)(24,75)
2,475,000 Fixed. (100,000)(St ) Floating.
10 4. The payments are always net. The contract
determines the cash flows timing as annual,
semiannual or monthly, etc. Every payment is the
net of the two cash flows
115. How to resolve problems Swaps are Over The
Counter (OTC) agreements. Therefore, the two
parties always face credit risk operational risk,
etc. Moreover, liquidity issues such as getting
out of the agreement, default possiblilities,
selling one side of the contract, etc., are
frequently encountered problems.
12Typical Uses of anInterest Rate Swap
 Converting a liability from
 fixed rate to floating rate
 floating rate to fixed rate
 Converting an investment from
 fixed rate to floating rate
 floating rate to fixed rate
13Why SWAPS The goals of entering a swap
are 1. Cost saving. 2. Changing the
nature of cash flow each party receives or
pays from fixed to floating and vice versa.
14INTEREST RATE SWAPS Example Plain Vanilla
Fixed for Floating rates swap A swap is to
begin in two weeks.Party A will pay a fixed rate
7.19 per annum on a semiannual basis, and will
receive the floating rate sixmonth LIBOR
30bps from from Party B. The notional principal
is EUR35million. The swap is for five years.Two
weeks later, the sixmonth LIBOR rate is 6.45
per annum.
15 The fixed rate in a swap is usually quoted on a
 semiannual bond equivalent yield
 basis. Therefore, the amount that is paid every
six months is
This calculation is based on the assumption that
the payment is every 182 days.
16 The floating side is quoted as a money market
yield basis. Therefore, the first payment is
Other future payments will be determined every 6
months by the sixmonth LIBOR at that time.
17 7.19
Party A
Party B
LIBOR 30 bps
 As in any SWAP, the payments
 are netted.
 In this case, the first payment is
 Party A pays Party B the net difference
 EUR1,254,802.74  EUR1,194,375.00
EUR60,427.74. 
18Another Example of a Plain Vanilla Interest
Rate Swap
 An agreement by Microsoft to receive 6month
LIBOR pay a fixed rate of 5 per annum every 6
months for 3 years on a notional principal of
USD100 million  Nextillustrates cash flows
19The principal amount USD100.000.000. The
cash flows are... semiannual
5 FIXED
SWAP DEALER
MICROSOFT
6month LIBOR
20Cash Flows to Microsoft(See Table 6.1, page 127)
Millions of USD
LIBOR
FLOATING
FIXED
Net
Date
Rate
Cash Flow
Cash Flow
Cash Flow
Mar.5, 2001
4.2
Sept. 5, 2001
4.8
2.10
2.50
0.40
Mar.5, 2002
5.3
2.40
2.50
0.10
Sept. 5, 2002
5.5
2.65
2.50
0.15
Mar.5, 2003
5.6
2.75
2.50
0.25
Sept. 5, 2003
5.9
2.80
2.50
0.30
Mar.5, 2004
6.4
2.95
2.50
0.45
21Intel and Microsoft (MS) Transform a
Liability(Figure 6.2, page 128)
5
5.2
MS
Intel
LIBOR0.1
LIBOR
22SWAP DEALER is Involved(Figure 6.4, page 129)
4.985
5.015
5.2
SD
Intel
MS
LIBOR0.1
LIBOR
LIBOR
23Intel and Microsoft (MS) Transform an
Asset(Figure 6.3, page 128)
5
4.7
Intel
MS
LIBOR0.25
LIBOR
24SWAP DEALER is Involved(See Figure 6.5, page 129)
5.015
4.985
4.7
SD
MS
Intel
LIBOR0.25
LIBOR
LIBOR
25 These examples illustrate five points
 1. In interest rate swaps, payments are netted.
In the example, Party A sent Party B a payment
for the net amount.  2. In an interest rate swap, the principal amount
is not exchanged. This is why the term notional
principal is used.  3. Party A is exposed to the risk that Party B
might default. Conversely, Party B is exposed to
the risk of Party A defaulting. If one party
defaults, the swap usually terminates.
26 4. On the fixed payment side, a 365day year is
used, while on the floating payment side, a
360day year is used. The number of days in the
year is one of the issues specified in the swap
contract.  5. Future payments are not known in advance,
because they depend on future realizations of the
Sixmonth LIBOR.  Estimates of future LIBOR values are obtained
from LIBOR yield curves which are based on Euro
Strip of Euro dollar futures strips.
27The Comparative Advantage Argument A firm has an
ABSOLUTE ADVANTAGE if it can obtain better rates
in both the fixed and the floating rate
markets.Firm A has a RELATIVE ADVANTAGE in one
market if the difference between what firm A
pays more than firm B in the floating rate
(fixed rate) market is less than the difference
between what firm A pays more than firm B in the
fixed rates (floating rate) market.
28Example A FIXED FOR FLOATING SWAP Two firms
need EUR10M financing for projects. They face the
following interest rates PARTY FIXED RATE
FLOATING RATE F1 15 LIBOR
2 F2 12 LIBOR 1 F2 HAS
ABSOLUTE ADVANTAGE in both markets, but F2 has
RELATIVE ADVANTAGE only in the market for fixed
rates. WHY The difference between what F1 pays
more than F2 in floating rates, (1), is less
than the difference between what F1 pays more
than F2 in fixed rates, (3).
29Now, suppose that the firms decide to enter a
FIXED for FLOATING swap based on the notional of
EUR10.000.000. The cash flows Annual payments
to be made on the first business day in March for
the next five years. The SWAP always begins with
each party borrowing capital in the market in
which it has a RELATIVE ADVANTAGE. Thus F1
borrows S EUR10,000,000 in the market for
floating rates, I.e., for LIBOR 2 for 5
years. F2 borrows EUR10,000,000 in the market
for fixed rates, I.e., for 12. NOW THE TWO
PARTIES EXCHANGE THE TYPE OF CASH FLOWS BY
ENTERING THE SWAP FOR FIVE YEARS.
30A fundamental implicit assumption The swap will
take place only if F1 wishes to borrow capital
for a FIXED RATE, While F2 wishes to borrow
capital for a FLOATING RATE. That is, both firms
want to change the nature of their payments.
31 FIXED FOR FLOATING SWAP
 A DIRECT SWAP
 FIRM FIXED RATE FLOATING RATE
 F1 15 LIBOR 2
 F2 12 LIBOR 1

LIBOR
LIBOR2
12
F2
F1
12
The result of the swap F1 pays fixed 14,
better than 15. F2 pays floating LIBOR,
better than LIBOR 1
322. AN INDIRECT SWAP with a SWAP DEALER FIRM
FIXED RATE FLOATING RATE F1 15
LIBOR 2 F2 12 LIBOR 1
SD
L25bps
L
L 2
12
F2
F1
12
12,25
F1 pays 14,25 fixed Better than 15. F2
pays L25bps Better than L1. The swap
dealer gains 50 bps 50,000.
33Notice that the two swaps presented above are two
possible contractual agreements. The direct, as
well as the indirect swaps, may end up
differently, depending on the negotiation power
of the parties involved. Nowadays, it is very
probable for swap dealers to be happy with 10
basis points. In the present example, another
possible swap arrangement is
L5bp L
L2
F2
F1
12
SD
12 125bp
Clearly, there exist many other possible swaps
between the two firms in this example.
34 Warehousing
 In practice, a swap dealer intermediating (making
a market in) swaps may not be able to find an
immediate offsetting swap. Most dealers will
warehouse the swap and use interest rate
derivatives to hedge their risk exposure until
they can find an offsetting swap. In practice,
it is not always possible to find a second swap
with the same maturity and notional principal as
the first swap, implying that the institution
making a market in swaps has a residual exposure.
The relatively narrow bid/ask spread in the
interest rate swap market implies that to make a
profit, effective interest rate risk management
is essential.
35EXAMPLE A RISK MANAGEMENT SWAP
BONDS MARKET
FL1 6MONTH BANK RATE. FL2 6MONTH LIBOR.
FL1
LOAN
10
SWAP DEALER A
BANK
FL2
LOAN
12
FIRM A BORROWS AT A FIXED RATE FOR 5 YEARS
36THE BANKS CASH FLOW 12  FLOATING1 FLOATING2
10 2 SPREAD Where the SPREAD FLOATING2
 FLOATING1 RESULTS THE BANK EXCHANGES THE
RISK ASSOCIATED WITH THE DIFFERENCE BETWEEN
FLOATING1 and 12 WITH THE RISK ASSOCIATED WITH
THE SPREAD FLOATING2  FLOATING1. The bank
may decide to swap the SPREAD for fixed,
riskfree cash flows.
37EXAMPLE A RISK MANAGEMENT SWAP
BOND MARKET
FL1
10
SWAP DEALER A
BANK
FL2
FL2
FL1
SWAP DEALER B
12
FIRM A
38THE BANKS CASH FLOW 12  FL1 FL2 10
(FL1  FL2 ) 2 RESULTS THE BANK EXCHANGES
THE RISK ASSOCIATED WITH THE SPREAD FL2 
FL1 WITH A FIXED RATE OF 2. THIS RATE IS A
FIXED RATE!
39 PRICING SWAPS
 The swap coupons (payments) for shortdated
fixedforfloating interest rate swaps are
routinely priced off the Eurodollar futures strip
(Euro strip). This pricing method works provided
that (1)Eurodollar futures exist.  (2)The futures are liquid.
 As of June 1992, threemonth Eurodollar futures
are traded in quarterly cycles  March, June,
September, and December  with delivery (final
settlement) dates as far forward as five years.
Most times they are liquid out to at least four
years.
40 The Euro strip is a series of successive
threemonth Eurodollar futures contracts.  While identical contracts trade on different
futures exchanges, the International Monetary
Market (IMM) is the most widely used. It is worth
mentioning that the Eurodollar futures are the
most heavily traded futures anywhere in the
world. This is partly as a consequence of swap
dealers transactions in these markets. Swap
dealers synthesize shortdated swaps to hedge
unmatched swap books and/or to arbitrage between
real and synthetic swaps.
41 Eurodollar futures provide a way to do that. The
prices of these futures imply unbiased estimates
of threemonth LIBOR expected to prevail at
various points in the future. Thus, they are
conveniently used as estimated rates for the
floating cash flows of the swap. The swap fixed
coupon that equates the present value of the
fixed leg with the present value of the floating
leg based on these unbiased estimates of future
values of LIBOR is then the  dealers mid rate.
42 The estimation of a fair mid rate is
complicated a bit by the facts that  The convention is to quote swap coupons for
generic swaps on a semiannual bond basis, and  The floating leg, if pegged to LIBOR, is usually
quoted on a money market basis.  Note that on very shortdated swaps the swap
coupon is often quoted on a money market basis.
For consistency, however, we assume throughout
that the swap coupon is quoted on a bond basis.
43 The procedure by which the dealer would obtain an
unbiased mid rate for pricing the swap coupon
involves three steps.  The first step Use the implied threemonth LIBOR
rates from the Euro strip to obtain the implied
annual effective LIBOR for the fulltenor of the
swap.  The second step Convert this fulltenor LIBOR to
an effective rate quoted on an annual bond basis.
 The third step Restate this effective bond basis
rate on the actual payment frequency of the swap.
44 NOTATIONS The swap is an mmonths or m/12 years
swap. The swap is to be priced off threemonth
Eurodollar futures, thus, pricing requires n
sequential futures series. n m/3 m 3n.  Step 1 Use the futures Euro strip to Calculate
the implied effective annual LIBOR for the full
tenor of the swap
45 N(t) is the total number of days covered by the
swap, which is equal to the sum of the actual
number of days in the succession of Eurodollar
futures.  Step 2 Convert the fulltenor LIBOR, which is
quoted on a money market basis, to its fixedrate
equivalent FRE(0,3n), which is stated as an
effective annual rate on an annual bond basis.
This simply reflects the different number of days
underlying bond basis and money market basis
46Step 3 Restate the fixedrate on the same
payment frequency as the floating leg of the
swap. The result is the swap coupon, SC. Let f
denote the payment frequency, then the coupon
swap is given by
47 Example For illustration purposes let us observe
Eurodollar futures settlement prices on April 24,
2001.  Eurodollar Futures Settlement Prices April
24,2001.  CONTRACT PRICE LIBOR FORWARD DAYS
 JUN01 95.88 4.12 0,3 92
 SEP01 95.94 4.06 3,6 91
 DEC01 95.69 4.31 6,9 90
 MAR02 95.49 4.51 9,12 92
 JUN02 95.18 4.82 12,15 92
 SEP02 94.92 5.08 15,18 91
 DEC02 94.64 5.36 18,21 91
 MAR03 94.52 5.48 21,24 92
 JUN03 94.36 5.64 24,27 92
 SEP03 94.26 5.74 27,30 91
 DEC03 94.11 5.89 30,33 90
 MAR04 94.10 5.90 33,36 92
 JUN04 94.02 5.98 36,39 92
 SEP04 93.95 6.05 39,42 91
48 These contracts imply the threemonth LIBOR (3M
LIBOR) rates expected to prevail at the time of
the Eurodollar futures contracts final
settlement, which is the third Wednesday of the
contract month. By convention, the implied rate
for threemonth LIBOR is found by deducting the
price of the contract from 100. Threemonth LIBOR
for JUN 01 is a spot rate, but all the others are
forward rates implied by the Eurodollar futures
price. Thus, the contracts imply the 3M LIBOR
expected to prevail three months forward, (3,6)
the 3M LIBOR expected to prevail six months
forward, (6,9), and so on. The first number
indicates the month of commencement (i.e., the
month that the underlying Eurodollar deposit is
lent) and the second number indicates the month
of maturity (i.e., the month that the underlying
Eurodollar deposit is repaid). Both dates are
measured in months forward.
49 In summary, the spot 3M LIBOR is denoted r 0,3 ,
the corresponding forward rates are denoted r3,6,
r6,9, and so on.  Under the FORWARD column, the first month
represents the starting month and the second
month represents the ending month, both
referenced from the current month, JUNE, which is
treated as month zero.  Eurodollar futures contracts assume a deposit of
91 days even though any actual threemonth period
may have as few as 90 days and as many as 92
days. For purposes of pricing swaps, the actual
number of days in a threemonth period is used in
lieu of the 91 days assumed by the futures. This
may introduce a very small discrepancy between
the performance of a real swap and the
performance of a synthetic swap created from a
Euro strip.
50 Suppose that we want to price a oneyear
fixedforfloating interest rate swap against 3M
LIBOR.  The fixed rate will be paid quarterly and,
therefore, is quoted quarterly on bond basis.  We need to find the fixed rate that has the same
present value (in an expected value sense) as
four successive 3M LIBOR payments.  Step 1 The oneyear implied LIBOR rate, based on
k 360/365,  m 12, n 4 and
 f4
 is
51(No Transcript)
52The swaps coupon is the dealer mid rate. To this
rate , the dealer will add several basis points.
53 Next, suppose that the swap is for semiannual
payments against 6month LIBOR. The first two
steps are the same as in the previous example.  Step 3 is different because f 2, instead of 4.
544.35 FIXED
Swap dealer
Client
6M LIBOR FLOATING
55 The procedure above allows a dealer to quote
swaps having tenors out to the limit of the
liquidity of Eurodollar futures on any payment
frequency desired and to fully hedge those swaps
in the Euro Strip.  The latter is accomplished by purchasing the
components of the Euro Strip to hedge a
dealerpaysfixedrate swap or, selling the
components of the Euro Strip to hedge a
dealerpaysfloatingrate swap.  Example Suppose that a dealer wants to price a
threeyear swap with a semiannual coupon when the
floating leg is sixmonth LIBOR. Three years
m36 months requiring 12 separate Eurodollar
futures n 12. Further, f 2 and the actual
number of days covered by the swap is N(t)
1096.  Step 1 The implied LIBOR rate for the entire
period of the swap
56(No Transcript)
57Step 2 The Fixed Rate Equivalent effective
annual rate on a bond basis is FRE
(5.17)(365/360) 5.24. Finally, Step 3 The
equivalent semiannual Swap Coupon is
calculated SC (1.0524).5 1(2) 5.17.
58 The dealer can hedge the swap by buying or
selling, as appropriate, the 12 futures in the
Euro Strip.  The full set of fixedrate for 6M LIBOR swap
tenors out to three and onehalf years, having
semiannual payments, that can be created from the
Euro Strip are listed in the table below. The
swap fixed coupon represents the dealers mid
rate. To this mid rate, the dealer can be
expected to add several basis points if
fixedrate receiver, and deduct several basis
points if fixedrate payer. The par swap yield
curve out to three and onehalf years still needs
more points.
59Implied Swap Pricing Schedule Out To Three and
Onehalf Years as of April 24,2001 Tenor of
swap Swap coupon mid rate 6 12 4.35 18
24 30 36 5.17 42 All swaps
above are priced against 6month LIBOR flat and
assume that the notional principal is non
amortizing.
60 Swap Valuation The example below illustrates the
valuation of an interest rate swap, given the
coupon payments are known. Consider a financial
institution that receives fixed payments at the
annual rate 7.15 and pays floating payments in a
twoyear swap. Payments are made every six
months. Let B(0,T)PV of USD1.00 paid at
T. Let L(0,T)PV of 1EuroUSD paid at T. These
prices are derived from the Treasury and
Eurodollar term structures, respectively. The
data are
61(No Transcript)
62 The fixed side of the swap.
 At the first payment date, t1, the dollar value
of the payment is 
 where NP denotes the notional principal.
 The present value of receiving one dollar for
sure at date t1, is 0.9679. Therefore, the
present value of the first fixed swap payment is 

63 By repeating, this analysis, the present value of
all fixed payments is 
 VFIXED(0)
 NP(.9679)(.0715)(182/365)
 (.9362)(.0715)(183/365)
 (.9052)(.0715)(183/365)
 (.8749)(.0715)(182/365)
 NP.1317.
 This completes the fixed payment of the swap.

64 On the floating side of the swap, the pattern of
payments is similar to that of a floating rate
bond, with the important proviso that there is no
principal payment in a swap. Thus, when the
interest rate is set, the bond sells at par
value. Given that there is no principal payment,
we must subtract the present value of principal
from the principal itself. The present value of
the floating rate payments depends on L(0, t4) 
the present value of receiving one Eurodollar at
date t4
65 The value of the swap to the financial
institution is  Value of Swap VFIXED(0)  VFLOATING(0)

 NP.1317  .1316 (.0001)NP.
 If the notional principal is 45M, the value of
the swap is 4,500.  In this example, the Treasury bond prices are
used to discount the cash flows based on the
Treasury note rate. The Eurodollar discount
factors are used to measure the present value of
the LIBOR cash flows. This practice incorporates
the different risks implicit in these different
cash flow streams.  This completes the example.
66 SWAP VALUATION The general formula
 Consider a swap in which there are n payments
occurring on dates Tj, where the number of days
between payments is kj, j 1,, n. Let R be the
swap rate, expressed as a percent NP represents
the notional principal and B(0,Tj) is the
present value of receiving one dollar for sure at
date Tj.  The value of the fixed payments is
67 The value of the floating rate payments
 If the swap is already in existence, let denote
the pre specified LIBOR rate. At date T1, the
payment is  and a new LIBOR rate is set.
 On T1, the value of the remaining floating rate
payments is  NP NPL(T1, TN).
 where L(T1, TN) is the present value at date T1
of a Eurodollar deposit that pays one dollar at
date Tn.  We are now ready to calculate the total value of
the floating rate payments at date T1.
68 The value of the floating rate payments at date
T1 is 
 The value of the floating payments at date 0 is
the present value of 
69 2. If the swap is initiated at date 0, then the
above equation simplifies as follows  Let (0) denote the current LIBOR rate. By
definition
70(No Transcript)
71 IN CONCLUSION The value of the swap
 for the party receiving fixed and paying
 floating is the difference between the fixed
 and the floating values. For example, the
 value of a swap that is initiated at time 0 is
72 PAR SWAPS A par swap is a swap for which the
present value of the fixed payments equals the
present value of the floating payments, implying
that the net value of the swap is zero. Equating
the value of the fixed payments and the value of
the floating rate payments yields the FIXED RATE,
R, which makes the swap value zero.
73 PAR SWAP Valuation Consider a financial
institution that receives fixed payments at the
rate 7.15 per annum and pays floating payments
in a twoyear swap. Payments are made every six
months. The data are
74 PAR SWAP VALUATION
 Solve for R, the equation
 NP(R/100)(.9679)(182/365)
 (R/100)(.9362)(183/365)
 (R/100)(.9052)(183/365)
 (R/100)(.8749)(182/365)
 NP1  .8684
 The equality implies
 R/100 .1316/1.8421
 R 7.14 per annum.
752. CURRENCY SWAPS Nowadays markets are
global. Firms cannot operate with disregard to
international markets trends and prices. Capital
can be transfered from one country to another
rapidly and efficiently. Therefore, firms may
take advantage of international markets even if
their business is local. For example, a firm in
Denver CO. may find it cheaper to borrow money in
Europe, exchange it to USD and repay it later,
exchanging USD into EUR. Currency swaps are
basically, interest rate swaps accross
international borders.
76 Case Study of a currency swap
 IBM and The World Bank(1982)
 A famous example of an early currency Swap took
place  between IBM an the World Bank in August 1981,
with  Salomon Brothers as the intermediary. The
complete details  of the swap have never been published in full.
 The following description follows a paper
published by D.R.  Bock in Swap Finance, Euromoney Publications.
77 In the mid 1970s, IBM had issued bonds in German
 marks, DEM, and Swiss francs, CHF. The bonds
maturity  date was March 30, 1986. The issued amount of
the CHF  bond was CHF200 million, with a coupon rate of
6.1785  per annum. The issued amount of the DEM bond was
 DEM300 million with a coupon rate of 10 per
annum.  During 1981 the USD appreciated sharply against
both  currencies. The DEM, for example, fell in value
from  USD.5181/DEM in March 1980 to USD.3968/DEM in
 August 1981. Thus, coupon payments of DEM100 had
 fallen in USD cost from USD51.81 to USD39.68. The
 situation with the Swiss francs was the Same.
Thus, IBM  enjoyed a sudden, unexpected capital gain from
the  reduced USD value of its foreign debt
liabilities.
78 In the beginning of 1981, The World Bank wanted
to  borrow capital in German marks and Swiss francs
against  USD. Around that time, the World Bank had issued
 comparatively little USD paper and could raise
funds at an  attractive rate in the U.S. market. Both parties
could  benefit from USD for DEM and CHF swap. The World
Bank  would issue a USD bond and swap the proceeds
with  IBM for cash flows in CHF and DEM. The bond was
issued  by the World Bank on August 11, 1981, settling on
August  25, 1981. August 25, 1981 became the settlement
date  for the swap. The first annual payment under the
swap  Was determined to be on March 30, 1982 the next
 coupon date on IBMs bonds. I.e., 215 days,
rather than  360 from the swap starting date.
79 The swap was intermediated by Solomon Brothers.
The  first step was to calculate the value of the CHF
and DEM  cash flows. At that time, the annual yields on
similar  Bonds were at 8 and 11, respectively. The
initial  period of 215day meant that the discount factors
were  calculated as follows
Where y is the respective bond yield, 8 for the
CHF and 11 for the DEM and n is the number of
days till payment.
80 The discount factors were calculated
 Date Days CHF DEM
 3.30.82 215 .9550775 .9395764
 3.30.83 575 .8843310 .8464652
 3.30.84 935 .8188250 .7625813
 3.30.85 1295 .7581813 .6870102
 3.30.86 1655 .7020104 .6189281
81 Next, the bond values were calculated
 NPV(CHF) 12,375,000.9550775 .8843310
 .8188250 .7581813
 212,375,000.7020104

 CHF191,367,478.
 NPV(DEM) 30,000,000.9395764 .8464652
 .7625813.6870102 330,000,000.6189
2811 
 DEM301,315,273.
82 The terms of the swap were agreed upon on AUG 11,
 1981. Thus, The World Bank would have been left
 exposed to currency risk for two weeks until AUG
25.  The World Bank decided to hedge the above derived
 NPV amounts with 14days currency forwards.
Assuming  that these forwards were at USD.45872/CHF and
 USD.390625/DEM, The World Bank needed a total
 amount of USD87,783,247 to buy the CHF
 USD117,701,753 to buy the DEM
 a total of USD205,485,000. This amount needed
 to be divided up to the various payments. The
only  problem was that the first coupon payment was for
215  days, while the other payments were based on a
period  of 360 days.
83 Assuming that the bond carried a coupon rate of
16 per annum with intermediary commissions and
fees totaling 2.15, the net proceeds of .9785
per dollar meant that the USD amount of the bond
issue had to be  USD205,485,000/0.9785 USD210,000,000.
 The YTM on the World Bank bond was 16.8. As
mentioned above, the first coupon payment
involved 215 days only.  Therefore, the first coupon payment was equal to
 USD210,000,000(.16)215/360
 USD20,066,667.
84 The cash flows are summarized in the following
table  Date USD CHF DEM
 3.30.82 20,066,667 12,375,000 30,000,000
 3.30.83 33,600,000 12,375,000 30,000,000
 3.30.84 33,600,000 12,375,000 30,000,000
 3.30.85 33,600,000 12,375,000 30,000,000
 3.30.86 243,600,000 212,375,000 330,000,000
 YTM 8 11 16.8
 NPV 205,485,000 191,367,478 301,315,273
 By swapping its foreign interest payment
obligations for  USD obligations, IBM was no longer exposed to
 currency risk and could realize the capital gain
from the  dollar appreciation immediately. Moreover, The
World  Bank obtained CHF and GEM cheaper than it would
had  it gone to the currency markets directly.
85CHF200M CHF CUPON
DEM300M DEM CUPON
IBM
SWITZ
GERMANY
DEM CUPON
USD CUPON
CHF CUPON
WORLD BANK
USD CUPON
USD CAPITAL
IBM PAY RECEIVE RECEIVE Date
USD CHF DEM 3.30.82
20,066,667 12,375,000 30,000,000 3.30.83
33,600,000 12,375,000 30,000,000 3.30.84
33,600,000 12,375,000 30,000,000 3.30.85
33,600,000 12,375,000 30,000,000 3.30.86
243,600,000 212,375,000 330,000,000
USA
86THE ANALYSIS OF CURRENCY SWAPS F1 in country A
looks for financing a project in country B AT
THE SAME TIME F2 in country B, looks for
financing a project in country A
COUNTRY B F2 PROJECT OF F1
COUNTRY A F1 PROJECT OF F2
87CURRENCY SWAP IN TERMS OF THE BORROWING RAES,
EACH FIRM HAS COMPARATIVE ADVANTAGE ONLY IN
ONE COUNTRY, EVEN THOUGH IT MAY HAVE ABSOLUTE
ADVANTAGE IN BOTH COUNTRIES. THUS, EACH FIRM
WILL BORROW IN THE COUNTRY IN WHICH IT HAS
COMPARATIVE ADVANTAGE AND THEN, THEY EXCHANGE THE
PAYMENTS THROUGH A SWAP.
88 CURRENCY SWAP FIXED FOR FIXED CLP Chilean Peso
BR Brazilian Real Firm CH1, is a Chilean
firm who needs capital for a project in Brazil,
while, A Brazilian firm, BR2, needs capital for
a project in Chile. The market for fixed
interest rates in these countries makes a swap
beneficial for both firms as follows
89 FIRM CHILE BRAZIL CH1 CLP12 BR16
BR2 CLP15 BR17 CH1 has comparative
advantage in Chile only. CH1 borrows in Chile in
CLP and BR2 borrows in Brazil in BR. The swap
begins with the interchange of the principal
amounts at the current exchange rate. The figures
below show a direct swap between CH1 and BR2 as
well as an indirect swap. The swap terminates at
the end of the swap period when the original
principal amounts exchange hands once more.
90ASSUME THAT THE CURRENT EXCHANGE RATE IS BR1
CLP250 ASSUME THAT CH1 NEEDS BR10.000.000 FOR
ITS PROJECT IN BRAZIL AND THAT BR2 NEEDS EXACTLY
CLP2,5B FOR ITS PROJECT IN CHILE. Again FIRM CHI
LE BRAZIL CH1 12 R16 BR2 15 R17
91DIRECT SWAP FIXED FOR FIXED
BR15
CH1
BR2
CLP12
BR17
CLP12
CHILE CH1 BORROWS CLP2.5B AND DEPOSITS IT IN
BR2S ACCOUNT IN SANTIAGO
BRAZIL BR2 BORROWS BR10M AND DEPOSITS IT IN CH1S
ACCOUNT IN SAO PAULO
CH1 pays BR15 BR2 pays CLP12 BR2
92INDIRECT SWAP FIXED FOR FIXED
SWAP DEALER
BR15.50
CLP12
BR17
CLP14.50
CH1
BR2
BR17
CLP12
CHILE CH1 BORROWS CLP2.5B AND DEPOSITS IT IN
BR2S ACCOUNT IN SANTIAGO
BRAZIL BR2 BORROWS BR10M AND DEPOSITS IT IN
CH1S ACCOUNT IN SAO PAULO
93THE CASH FLOWS CH1 PAYS BR15.50 BR2 PAYS
CLP14.50 SWAP DELER CLP2.50
BR1.50 EXAMPLE CLP2,5B(0.025)
BR10M(0.015)(250) CLP62,500,000  CLP37,500,000
CLP25,000,000 Notice In this case, CH1 saves
0.25 and BR2 saves 0.25, while the SWAP DEALER
bears the exchange rate risk. If the CLP
depreciates against the BR the intermediarys
revenue declines. When the exchange rate reaches
CLP466,67/BR the intermediary gain is zero. If
the Chilean Peso continues to depreciate the
intermediary loses money on the deal.
94 Foreign Currency Swaps
 EXAMPLE a plain vanilla
 foreign currency swap.
 F1, an Italian firm has issued bonds with face
value of EUR50M with a annual coupon of 11.5,
paid semiannually and maturity of seven years.  F1 would prefer to have USD and to be making
interest payments in USD. Thus, F1 enters into a
foreign currency swap with F2  usually a SWAP
DEALER. In the first phase of the swap, F1
exchanges the principal amount of EUR50M with
party F2 and, in return, receives principal
worth USD60M. Usually, this exchange is done at
the current exchange rate, i.e.,  S USD1.20/EUR in this case.
95 The swap contract is as follows F1 agrees to
make semi annual interest rate payments to F2
at the rate of 9.35 per annum based on the USD
denominated principal for a  Seven Year period. In return, F1 receives from F2
a semi annual interest rate at the annual rate
of 11.5, based on the EURO denominated principal
for a seven years.  The swap terminates seven years later,
 when the principals are again exchanged
 F1 receives the principal amount of EUR50M
 F2 receives the principal amount of USD60M.
96DIRECT SWAP FIXED FOR FIXED
USD9.35
F1
F2
EUR11.5
EUR11.5
USD9.35
ITALY F1 BORROWS EUR50M AND DEPOSITS IT IN F2s
ACCOUNT IN MILAN
U.S.A F2 DEPOSITS USD60M IN F1S ACCOUNT IN NEW
YORK CITY
At maturity, the original principals are
exchanged to terminate the swap.
97 By entering into the foreign currency swap, F1
has successfully transferred its EUR liability
into a USD liability.  In this case, F2 payments to F1 were based on
the the same rate of partys F1 payments in Italy
EUR11.5. Thus, F1 was able to exactly offset the
EUR interest rate payments. This is not
necessarily always the case. It is quite
possible that the interest rate payments F1
receives from SWAP DEALER F2 only partially
offset the EUR expense. In the same example, the
situation may change to
98DIRECT SWAP FIXED FOR FIXED
USD9.55
F1
F2
EUR11.25
USD9.55
EUR11.5
U.S.A F2 DEPOSITS USD60M IN F1S ACCOUNT IN NEW
YORK CITY
ITALY F1 BORROWS EUR50M AND DEPOSITS IT IN F2s
ACCOUNT IN MILAN
At maturity, the original principals are
exchanged.
99EXAMPLE FIXED FOR FLOATING A Mexican firm needs
capital for a project in Great Britain and a
British firm needs capital for a project in
Mexico. They enter a swap because they can
exchange fixed interest rates into floating and
borrow at rates that are below the rates they
could obtain had they borrowed directly in the
same markets. In this case, the swap is
FixedforFloating rates, i.e., One firm
borrows fixed, the other borrows floating and
they swap the cash flows therby, changing the
nature of the payments from fixed to floating and
vice versa.
100A DIRECT SWAP FIXED FOR FLOATING INTEREST
RATES MEXICO GREAT BRITAIN MX1 MXP15 GBPLIB
OR 3 GB2 MXP18 GBPLIBOR 1 ASSUME The
current exchange rate is GBP1 MXP15. MX1
needs GBP5.000.000 in England GB2 needs
MXP75.000.000 in Mexico. THUS MX1 borrows MXP75M
in Mexico and deposits it in GB2s account in
Mexico D.F. While GB2 borrows GBP5,000,000 in
Great Britain and deposits it in MX1s account in
London.
101DIRECT SWAP FIXED FOR FLOATING
GBP L 1
MX1
GB2
MXP15
GBP L 1
MXP15
MEXICO MX1 BORROWS MXP75M AND DEPOSITS IT IN
GB2S ACCOUNT IN MEXICO D.F.
ENGLAND GB2 BORROWS GBP5,000,000 AND DEPOSITS IT
IN MX1S ACCOUNT IN LONDON,
MX1 pays GBP L1 GB2 pays MXP15
102DIRECT SWAP FIXED FOR FLOATING AGAIN MX1 pays
GBP L 1 GB2 pays MXP15. What does this
mean It means that both firms pay interest for
the capitals they borrowed in the markets where
each has comparative advantage. BUT, with the
swap, MX1 pays in pounds GBP L 1, a better
rate than GBP LIBOR 3, the rate it would have
paid had it borrowed directly in the floating
rate market in Great Britain. GB2 pays MXP15
fixed, which is better than the MXP18 it would
have paid had it borrowed directly in Mexico.
103 A CURRENCY SWAPS VALUATION
 Under the terms of a swap, party A receives EUR
interest rate payments and making USD interest
payments.  BEUR PV of the payments in EUR from party B,
including the principal payment at maturity.  BUSD PV of the payments in USD from party A,
including the principal payment at maturity.  S0(EUR/USD) the current exchange rate.
 Then, the value of the swap to counterparty A in
terms of Euros is  VEUR BEUR  S0(EUR/UED)BEUR.
104 Note that the value of the swap depends
 upon the shape of the domestic term
 structure of interest rates and the foreign
 term structure of interest rates.
 EXAMPLE A PLAIN VANILLA CURRENCY SWAP
VALUATION  Consider a financial institution that enters
 into a twoyear foreign currency swap for
 which the institution receives 5.875 per
 annum semiannually in EUR and pays 3.75
 per annum semiannually in USD.
105 The principals in the two currencies are
 EUR12M USD10M, reflecting the Current
 exchange rate S0(EUR/USD) 1.20
 Information about the US and ITALIAN term
 structures of interest rates is given in
 following table
106 Domestic and Foreign Term Structure
 Maturity Price of a zero coupon Bond
Months USD EUR  6 .0840 (3.22) .9699 (6.09)
 12 .9667 (3.38) .9456 (5.59)
 18 .9467 (3.65) .9190 (5.63)
 24 .9249 (3.90) .8922 (5.70)
 Figures in parenthesis are continuously
compounded yields.  The coupon payment of the semiannual interest
payments in EUR is
107 Therefore, the present value of the Interest rate
 payments in USD plus principal is
The coupon payment of the semiannual interest
payments in USD is
108 Therefore, the present value of the interest rate
 payments in USD plus principal is
109The value of the foreign currency swap is
1103.COMMODITY SWAPS The assets underlying the swaps
in these markets are agreed upon quantities of
the commodity. Here, we analyze commodity swaps
using mainly energy commodities natural gas and
crude oil. For example, 100,000 barrels of crude
oil.
111 How does a commodity swap works
 In a typical commodity swap
 party A makes periodic payments to counterparty B
at a fixed price per unit  for a given notional quantity of some commodity.
 B pays A an agreed upon floating price
 for the same notional quantity of the commodity
underlying the swap.  The commodities are usually the same.
 The floating price is usually defined as the
market price or an average market price, the
average being calculated using  spot commodity prices over
 some predefined period.
112 Example A Commodity Swap
 Consider a refinery that has a constant demand
for 30,000 barrels of oil per month and is
concerned about volatile oil prices. It enters
into a threeyear commodity swap with a swap
dealer. The current spot oil price is USD24.20
per barrel.  The refinery agrees to make monthly payments to
the swap dealer at a fixed price of USD24.20 per
barrel.  The swap dealer agrees to pay the refinery the
average daily price for oil during the CURRENT
month.  The notional principal is 30,000 barrels.
 The swap is for 36 months.
113Spot oil market
Daily Spot Price
Oil
USD24.20/bbl USD726,000
Swap Dealer
Refinery
Average Spot Price
The commodity 30,000 Barrels(1,000/day).
114SPOT OIL MARKET
Daily spot price
OIL
USD726,000
Swap Dealer A
Italian Refinery
Average spot price
USD726,000/1.2 EUR648,214
USD726,000
Swap Dealer B
115 Valuation of Commodity of Swaps
 In a plain vanilla commodity swap, counterparty
A agrees to pay counterparty B a fixed price,
P(fixed, ti), per unit of the commodity at dates
t1, t2,. . ., tn.  Counterparty B agrees to pay counterparty A the
spot price, S(ti) of the commodity at the same
dates t1, t2,. . ., tn.  The notional principal is NP units of the
commodity  The net payment to counterparty A at date t1
is  V(t1, t1) S(t1)  P(fixed, t1)NP.

116 The value of this payment at date 0 is the
 present Value of V(t1, t1)

 V(0, t1) PV0V(t1, t1)

 PV0S(t1) P(fixed, t1)B(0, t1)NP
 where B(0, t1) is the value at date 0 of
receiving  One dollar for sure at date t1. In the absence of
 Carrying Costs and convenience yields, the
 present value of the spot price S(t1) would be
 equal to the current spot price. In practice,
 however, there are carrying costs and
 convenience yields.
117 It can be shown that the use of forward prices
incorporates these carrying costs and convenience
yields. Drawing on this insight, an alternative
expression for the present value of the spot
price PV0S(t1) in terms of forward prices may
be derived as follows  Consider a forward contract that expires at date
t1 written on this commodity with the forward
price F(0, t1). The cash flow to the forward
contract when it expires at date t1 is  S(t1)  F(0, t1).
 The value of the forward contract at date 0 is
 PV0S(t1)  F(0, t1)B(0, t1).
118 Like any forward, the forward price is set
 such that no cash is exchanged when the
 contract is written. This implies that the
 value of the forward contract, when
 initiated, is zero. That is
 PV0S(t1) F(0, t1)B(0, t1).
 Using this expression, the value at date 0 of
 the first swap payment is
 V(0,tl) F(0,t1)  P(fixed,t1)B(0, tl)NP.
119 Repeating this argument for the remaining
payments, it can be shown that the  value of the commodity swap at date 0 is
Note that the value of the commodity swap in this
expression depends only on the forward prices,
F(0,tj), of the underlying commodity and the
zerocoupon bond prices, B(0, t1), all of which
are market prices observable at date 0.
120FINANCIAL ENGINEERING 1 From the derivatives
trading room of BP Hedging the sale and purchase
of Natural Gas, using NYMEX Natural Gas futures
and creating a sure profit margin Employing a
swap of the remaining spread.
121April 12 1145AM From BPs derivatives trading
room 1. The 1st call BP agrees to buy NG from BM
in August at the market price on AUG 12. 2. The
2nd call BP hedges the NG purchase going long
NYMEX SEP NG futures. 3. The 3rd call BP finds
a buyer for the gas  SST. But, SST negotiates
the purchase price, P, to be at some discount, X,
off the current SEP NYMEX NG futures. X is left
unknown for now. P F4.12,SEP  X
122A PARTIAL SUMMARY of BP POSITION
DATE SPOT
FUTURES
 April 12 CONTRACTS Long SEP NYMEX
 Buy from BM. Futures.
 SELL TO SST F4,12 SEP 6.87.
 August 12
 Buy NG from BM Short SEP NYMEX Futures.
 for S1 F8,12,SEP
 (ii) Sell NG to SST for
 P F4, 12 SEP X
 PARTIAL CASH FLOW ON AUG 12
 F4,12 SEP X S1 F 8,12 SEP  F4,12 SEP

 F 8,12 SEP S1  X
123How can BM eliminate the BASIS risk BP decides
to enter a swap. Clearly, this is a floating for
floating swap. 4. The 4th call BP enters a swap
whereby BP pays the Swap dealer F8,12,SEP
USD.09 and receives S1 from the Swap dealer.
The swap is described as follows
124A FLOATING FOR FLOATING SWAP
F8,12,SEP USD.09
SWAP DEALER
BP
S1
The principal amount underlying the swap is the
same amount of NG that BP buys from BM and sells
to SST.
125 SUMMARY OF CASH FLOWS ON AUG
12 MARKET CASH FLOW Spot F4, 12 SEP
 X  S1 Futures F 8, 12
SEP  F4, 12 SEP Swap  F
8,12 SEP USD.09 S1 TOTAL USD.09
 X.
126 BP decides to make 3 cents per
unit of NG. Solving USD.03 USD.09  X
yields X USD.06. 5. The 5th call BP calls
SST and agree on the purchase price. On AUG 12,
SST buys the NG from BP for P USD6.87 
USD.06 USD6.81.
127THE BP EXAMPLE
SWAP DEALER
MARKET
SWAP
S1
F8.12,SEP  .09
F4,12SEP  .06
S1
BM
SPOT
BP
SST
NG
NG
LONG F4,12SEP
SHORT F8.12,SEP
FUTURES
NYMEX
128 4. BASIS SWAPS A basis swap is a risk
management tool that allows a hedger to eliminate
the BASIS RISK associated with a hedge. Recall
that a firm faces the CASH PRICE RISK, opens a
hedge, using futures, in order to eliminate this
risk. In most cases, however, the hedger firm
will face the BASIS RISK when it operates in the
cash markets and closes out its futures hedging
position. We now show that if the firm wishes to
eliminate the basis risk, it may be able to do so
by entering a BASIS SWAP. In a BASIS SWAP, The
long hedger pays the initial basis, I.e., a
fixed payment and receives the terminal basis,
I.e., a floating payment. The short hedger, pays
the terminal basis and receives the initial
basis.
129 1. THE FUTURES SHORT HEDGE
 TIME CASH FUTURES BASIS
 0 S0 F0,T B0,T
S0  F0,T 
 k Sk Fk,T Bk,T Sk  Fk,T

 The selling price for the SHORT hedger is F0,T
Bk,T .  2. THE SWAP OF THE SHORT HEDGER

 3. THE SHORT HEDGERS SELLING PRICE
 F0,T Bk,T B0,T  Bk,T F0,T B0,T
 F0,T S0  F0,T
 S0 .
B0,T
SHORT HEDGER
SWAP DEALER
Bk,T
130 1. THE FUTURES LONG HEDGE
 TIME CASH FUTURES BASIS
 0 S0 F0,T B0,T
S0  F0,T 
 k Sk Fk,T Bk,T Sk  Fk,T

 The purchasing price for the LONG hedger is F0,T
Bk,T .  2. THE SWAP OF THE LONG HEDGER


 3. THE LONG HEDGERS PURCHASING PRICE
 F0,T Bk,T B0,T  Bk,T F0,T B0,T
 F0,T S0  F0,T
B0,T
LONG HEDGER
SWAP DEALER
Bk,T
1311. PRICE RISK
2. BASIS RISK
3. NO RISK AT ALL. THE CASH FLOW IS
THE CURRENT CASH PRICE!
FUTURES HEDGING
BASIS SWAP
132 BASIS SWAP
Buy NG at Screen  10
NYMEX
USD6.60
F
USD6.50
 10
POWER PLANT
GAS PRODUCER
SWAP DEALER
S  F
GAS
Power plant is a long hedger. B0 .10. BK
S F. Power plant may swap the bases and the
final purchasing price is USD6.60 S F S
 F (.10) USD6.50.
133FINANCIAL ENGINEERING 2. A Mexican firm. All
its costs in MXP are fixed for the next 5 years.
All its revenews in MXP are fixed for the next 5
years. The only floating cost is the cost of oil
it buys. The firm buys 150,000 barrels of crude
oil every 3 months in the market price and pays
in USD. It wishes to change this floating USD
payment into a fixed MXP payment. RECIEVE
PAY SWAP DEALER 1. FLOATING S 0,50 AVERAGE
(S) FIXED USD26/bbl USD25/bbl SWAP DEALER
2. FLOATING USD LIBOR USD LIBOR
25pbs FIXED 11 10 (USD3.9M) SWAP DEALER
3. FLOATING USD LIBOR25pbs LIBOR FIXED 8(MXP
37.181.898) MXP35M THE FIRM FLOATING AVERAGE (S)
S FIXED USD26/bbl USD3.9M All
payments are quartely payments. The swap is for
20 quarterly cash flows.
134The swap Quarterly payments for the next 5 years
OIL PRODUCERS
USD156M USD3.9M/0.025
150,000bbls
150,000bbls USD S
USD26/bbl Total USD3.9M
USD3.9M
SWAP DEALER INTEREST RATES
MEXICAN FIRM
SWAP DEALER COMMODITY
USD ave(S)
USD LIBOR
MXP37,181,898 USD LIBOR
SWAP DEALER FORX
NPV3.9/(1.025)t USD60,797,733 EXCHANGE
USD1MXP10 MXP607,977,330 MXP607,977,330C/(1.02
)t C MXP37,181,898
USD156M
MXP1,859,094,907 MXP37,181,898/0.02