Swaps Chapter 6

1
SwapsChapter 6
2
SWAPS 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.
3
SWAPSA 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
4
It 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.

6
2. 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
7
2. 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.
8
3. 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
9
3. 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
11
5. 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.
12
Typical 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

13
Why 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.
14
INTEREST 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 semi-annual basis, and will
receive the floating rate six-month LIBOR
30bps from from Party B. The notional principal
is EUR35million. The swap is for five years.Two
weeks later, the six-month LIBOR rate is 6.45
per annum.
15

• The fixed rate in a swap is usually quoted on a
• semi-annual 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 six-month 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.
•  

18
Another Example of a Plain Vanilla Interest
Rate Swap

• An agreement by Microsoft to receive 6-month
  LIBOR pay a fixed rate of 5 per annum every 6
  months for 3 years on a notional principal of
  USD100 million
• Next slide illustrates cash flows

19
The principal amount USD100.000.000. The
cash flows are... semiannual
5 FIXED
SWAP DEALER
MICROSOFT
6-month LIBOR
20
Cash 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
21
Intel and Microsoft (MS) Transform a
Liability(Figure 6.2, page 128)
5
5.2
MS
Intel
LIBOR0.1
LIBOR
22
SWAP DEALER is Involved(Figure 6.4, page 129)

4.985
5.015
5.2
SD
Intel
MS
LIBOR0.1
LIBOR
LIBOR
23
Intel and Microsoft (MS) Transform an
Asset(Figure 6.3, page 128)

5
4.7
Intel
MS
LIBOR-0.25
LIBOR
24
SWAP DEALER is Involved(See Figure 6.5, page 129)

5.015
4.985
4.7
SD
MS
Intel
LIBOR-0.25
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 365-day year is
  used, while on the floating payment side, a
  360-day 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
  Six-month LIBOR.
• Estimates of future LIBOR values are obtained
  from LIBOR yield curves which are based on Euro
  Strip of Euro dollar futures strips.

27
The 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.
28
Example 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).
29
Now, 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.
30
A 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
32
2. 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.
33
Notice 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 off-setting swap. Most dealers will
  warehouse the swap and use interest rate
  derivatives to hedge their risk exposure until
  they can find an off-setting 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.

35
EXAMPLE A RISK MANAGEMENT SWAP
BONDS MARKET
FL1 6-MONTH BANK RATE. FL2 6-MONTH LIBOR.
FL1
LOAN
10
SWAP DEALER A
BANK

FL2
LOAN
12
FIRM A BORROWS AT A FIXED RATE FOR 5 YEARS
36
THE 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,
risk-free cash flows.
37
EXAMPLE A RISK MANAGEMENT SWAP
BOND MARKET
FL1
10
SWAP DEALER A
BANK

FL2
FL2
FL1
SWAP DEALER B
12
FIRM A
38
THE 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 short-dated
  fixed-for-floating 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, three-month 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
  three-month 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 short-dated 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 three-month 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 short-dated 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 three-month LIBOR
  rates from the Euro strip to obtain the implied
  annual effective LIBOR for the full-tenor of the
  swap.
• The second step Convert this full-tenor 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 m-months or m/12 years
  swap. The swap is to be priced off three-month
  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 full-tenor LIBOR, which is
  quoted on a money market basis, to its fixed-rate
  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

46
Step 3 Restate the fixed-rate 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 three-month LIBOR (3-M
  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 three-month LIBOR is found by deducting the
  price of the contract from 100. Three-month 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 3-M LIBOR
  expected to prevail three months forward, (3,6)
  the 3-M 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 3-M 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 three-month 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 three-month 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 one-year
  fixed-for-floating interest rate swap against 3-M
  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 3-M LIBOR payments.
• Step 1 The one-year implied LIBOR rate, based on
  k 360/365,
• m 12, n 4 and
• f4
• is

51
(No Transcript)
52

• Step 2 and 3

The 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 6-month LIBOR. The first two
  steps are the same as in the previous example.
• Step 3 is different because f 2, instead of 4.

54
4.35 FIXED
Swap dealer
Client
6-M 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
  dealer-pays-fixed-rate swap or, selling the
  components of the Euro Strip to hedge a
  dealer-pays-floating-rate swap.
• Example Suppose that a dealer wants to price a
  three-year swap with a semiannual coupon when the
  floating leg is six-month 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)
57
Step 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 fixed-rate for 6-M LIBOR swap
  tenors out to three and one-half years, having
  semiannual payments, that can be created from the
  Euro Strip are listed in the table below. The
  swap fixed coupon represents the dealer's mid
  rate. To this mid rate, the dealer can be
  expected to add several basis points if
  fixed-rate receiver, and deduct several basis
  points if fixed-rate payer. The par swap yield
  curve out to three and one-half years still needs
  more points.

59
Implied Swap Pricing Schedule Out To Three and
One-half 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 6-month 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
two-year 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 two-year 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.

75
2. 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 IBM's 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 215-day 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 14-days 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.

85

• THE SWAP

CHF200M 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
86
THE 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
87
CURRENCY 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.
90
ASSUME 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
91
DIRECT 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
92
INDIRECT 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
93
THE 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 semi-annually 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.

96
DIRECT 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

98
DIRECT 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.
99
EXAMPLE 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
Fixed-for-Floating 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.
100
A 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.
101
DIRECT 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
102
DIRECT 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 two-year foreign currency swap for
• which the institution receives 5.875 per
• annum semiannually in EUR and pays 3.75
• per annum semi-annually 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 semi-annual 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 semi-annual interest
payments in USD is
108

• Therefore, the present value of the interest rate
• payments in USD plus principal is

109
The value of the foreign currency swap is
110
3.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 three-year 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.

113
Spot 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).
114
SPOT 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
zero-coupon bond prices, B(0, t1), all of which
are market prices observable at date 0.
120
FINANCIAL 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.
121
April 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
122
A 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

123
How 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
124
A 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.
127
THE 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
131
1. 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.
133
FINANCIAL 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.
134
The 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
NPV?3.9/(1.025)t USD60,797,733 EXCHANGE
USD1MXP10 MXP607,977,330 MXP607,977,330?C/(1.02
)t C MXP37,181,898
USD156M
MXP1,859,094,907 MXP37,181,898/0.02