1

Swaps

Chapter 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

SWAPS

A 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 involves1. Two parties2. An underlying asset3. Cash flows4. A payment schedule5. 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 oilAn equity index

7

2. The Underlying asset is called the

NOTIONAL AMOUNTOr

The PRINCIPALBecause it only serves to determine the cashflows. Neither party needs to own it and it

almost

never changes hands.

8

3. The cash flowsmay 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 flowsThe interest rates, fixed or floating,

multiply the notional amount in order to determine the cash flows.

Ex: ($10M)(.07)=$700,000; Fixed.($10M)(Lt+30bps); 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 riskoperational 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

1. 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:

02.74.EUR1,254,8 100

19.7

365

(182)000EUR35,000,

100

Rate Fixed

Period

in Days

amount

Notional

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:

75.EUR1,194,3 100

.30)45.6(

360

(182)000EUR35,000,

100

Rate Floating

Period

in Days

amount

Notional

Other future payments will be determined every 6 months by the six-

month LIBOR at that time.

17

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.

 

Party A Party B

7.19%

LIBOR + 30 bps

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

MICROSOFT

SWAP DEALER

5% FIXED

6-month LIBOR

20

---------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

Cash Flows to Microsoft(See Table 6.1, page 127)

21

Intel and Microsoft (MS) Transform a Liability

(Figure 6.2, page 128)

Intel MS

LIBOR

5%

LIBOR+0.1%

5.2%

22

SWAP DEALER is Involved(Figure 6.4, page 129)

SD

LIBOR LIBORLIBOR+0.1%

4.985% 5.015%

5.2%Intel MS

23

Intel and Microsoft (MS) Transform an Asset

(Figure 6.3, page 128)

Intel MS

LIBOR

5%

LIBOR-0.25%

4.7%

24

SWAP DEALER is Involved(See Figure 6.5, page 129)

Intel SD MS

LIBOR LIBOR

4.7%

5.015%4.985%

LIBOR-0.25%

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

1. A DIRECT SWAP:

FIRM FIXED RATE FLOATING RATE

F1 15% LIBOR + 2%

F2 12% LIBOR + 1%

F2 F112%

LIBOR LIBOR+2%

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%

F2 F1SD12%

L+25bps L L + 2%

12% 12,25%

F1 pays 14,25% fixed: Better than 15%. F2 pays L+25bps : Better than L+1%. 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:

F2 F1L+5bp L

12% 12%+5bp

Clearly, there exist many other possible swaps between the two firms in this

example.

L+2%12%SD

34

WarehousingIn 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

BANK

12%

10%

FIRM A BORROWS AT A FIXED RATE FOR 5 YEARS

FL1

SWAP DEALER A

FL2

LOAN

LOAN

FL1 = 6-MONTH BANK RATE.

FL2 = 6-MONTH LIBOR.

36

THE BANK’S 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

BANK

12%

10% FL1

SWAP DEALER A

FL2

SWAP DEALER BFL1

FL2

FIRM A

38

THE BANK’S 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 SWAPSThe 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

dealer’s mid rate.

42

The estimation of a “fair” mid rate is complicated a bit by the facts that:

(1)The convention is to quote swap coupons for generic swaps on a semiannual bond basis, and

(2)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:

futures. Eurodollarth - tby the covered days of

number actual thedenotes N(t);N(t)

360k

where1,)]360

N(t)(r [1r

kn

1t1),3(t)-3(t0,3n

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:

.360

365rFRE(0,3n) 0,3n

46

1}(f).]360

365r{[1 SC

:as rewritten be can FRE(0,3n),

of onsubstituti upon which,

1}(f), - FRE(0,3n)]{[1 SC

f

1

0,3n

f

1

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 DAYSJUN01 95.88 4.12 0,3 92SEP01 95.94 4.06 3,6 91DEC01 95.69 4.31 6,9 90MAR02 95.49 4.51 9,12 92JUN02 95.18 4.82 12,15 92SEP02 94.92 5.08 15,18 91DEC02 94.64 5.36 18,21 91MAR03 94.52 5.48 21,24 92JUN03 94.36 5.64 24,27 92SEP03 94.26 5.74 27,30 91DEC03 94.11 5.89 30,33 90MAR04 94.10 5.90 33,36 92JUN04 94.02 5.98 36,39 92SEP04 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 f=4

is:

51

basis.market money on 4.34%,

1

)360

92.0451)(1

360

90.0431(1

)360

91.0406)(1

360

92.0412(1

1)]360

N(t)(r [1r

365

360

kn

1t1),3(t)-3(t0,3n

52

Step 2 and 3:

basis. bondquarterly

aon 4.33%1}(4)]360

3654340.{[1

1}(f)]360

365r{[1 SC

:asrewritten becan FRE(0,3n), ofon substituti

upon which,1}(f), - FRE(0,3n)]{[1 SC

4

1

f

1

0,3n

f

1

The swap’s 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

Client Swap dealer

4.35% FIXED

6-M LIBOR FLOATING

basis. bond

semiannuala on 4.35%, SC

);2)](1)360

365(.0434[1 SC 2

1

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: m=36 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

basis.market money on 5.17%,

1

)360

92.0590)(1

360

90.0589)(1

360

91.0574(1

)360

92.0564)(1

360

92.0548)(1

360

91.0536(1

)360

91.0508)(1

360

92.0482)(1

360

92.0451(1

)360

90.0431)(1

360

91.0406)(1

360

92.0412(1

1)]360

N(t)(r [1r

1096

360

1096

36012

1t1),3(t)-3(t0,36

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 ValuationThe 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

Payments dates

Days between payment

Dates

Treasury Bills Prices

B(0,T)

Eurodollar

Deposit

L(0,T)

t1 = 182

t2 = 365

t3 = 548

t4 = 730

182

183

183

182

.9679

.9362

.9052

.8749

.9669

.9338

.9010

.8684

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:

 

,365

182(.0715)N)t,(tV P11FIXED

).t,(tV]9679[.)t(0,V 11R1FIXED

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:

.(.1316)N

]8684.1[N

)]t[L(0,NN(0)V

P

P

4PPFLOATING

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 formulaConsider 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:

n

1j

jjPFIXED ]}.

365

k][

100

R)[T{B(0,N(0)V

67

The value of the floating rate payments:1. If the swap is already in existence, let λ

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 – NP{L(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.  

]360

k[λN 1

P

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: 

).T,L(TNN 360

kλN)(TV

n1PP

1P1FLOATING

).TL(0, )T)L(0,T,L(T because trueholds This

).TL(0,N-)TL(0,1360

kλN (0)V

:)(TV

n1n1

nP11

PFLOATING

1FLOATING

69

2. If the swap is initiated at date 0, then the above equation simplifies as follows:

Let λ(0) denote the current LIBOR rate. By definition:

:is payments rate

floating theof value the,Tk

because and

360T

λ(0)1

1)TL(0,

11

11

70

)].T L(0,-[1N (0)V

).TL(0,N-

)TL(0,1360

Tλ(0)N (0)V

nPFLOATING

nP

11

PFLOATING

71

IN CONCLUSION: The value of the swapfor the party receiving fixed and payingfloating is the difference between the fixedand the floating values. For example, thevalue of a swap that is initiated at time 0 is:

.]TL(0,[1N]}365

k][

100

R)[T{B(0,N

(0)V - (0)V V

:is floating paying and fixed receiving

party for the VALUE SWAP THE

n

1jnP

jjP

FLOATINGFIXEDSWAP

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.

.]TL(0,[1N]}365

k][

100

R)[T{B(0,N

(0)V (0)V

:SWAP For PAR

n

1jnP

jjP

FLOATINGFIXED

73

Payments dates

Days between payment

Dates

Treasury Bills Prices

B(0,T)

Euro

Dollar Deposit

L(0,T)

t1 = 182

t2 = 365

t3 = 548

t4 = 730

182

183

183

182

.9679

.9362

.9052

.8749

.9669

.9338

.9010

.8684

PAR SWAP ValuationConsider 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)]

= NP[1 - .8684]The equality implies:

R/100 = .1316/1.8421R = 7.14% per annum.

75

2. CURRENCY SWAPSNowadays 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

placebetween IBM an the World Bank in August 1981, withSalomon Brothers as the intermediary. The complete

detailsof 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 Germanmarks, DEM, and Swiss francs, CHF. The bonds maturitydate was March 30, 1986. The issued amount of the CHFbond 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 toborrow 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 anattractive rate in the U.S. market. Both parties could benefit from USD for DEM and CHF swap. The World Bankwould issue a USD bond and swap the $ proceeds withIBM for cash flows in CHF and DEM. The bond was issued by the World Bank on August 11, 1981, settling on August25, 1981. August 25, 1981 became the settlement datefor 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. Thefirst step was to calculate the value of the CHF and

DEM cash flows. At that time, the annual yields on similarBonds were at 8% and 11%, respectively. The initialperiod of 215-day meant that the discount factors werecalculated as follows:

,

y)(1

1actorDiscount F

360

n

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 DEM3.30.82 215 .9550775 .93957643.30.83 575 .8843310 .84646523.30.84 935 .8188250 .76258133.30.85 1295 .7581813 .68701023.30.86 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[.61892811]

= DEM301,315,273.

82

The terms of the swap were agreed upon on AUG 11,1981. Thus, The World Bank would have been leftexposed 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.

Assumingthat these forwards were at USD.45872/CHF andUSD.390625/DEM, The World Bank needed a totalamount 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 onlyproblem was that the first coupon payment was for 215days, 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 DEM3.30.82 20,066,667 12,375,000 30,000,0003.30.83 33,600,000 12,375,000 30,000,0003.30.84 33,600,000 12,375,000 30,000,0003.30.85 33,600,000 12,375,000 30,000,0003.30.86 243,600,000 212,375,000 330,000,000YTM 8% 11% 16.8%NPV 205,485,000 191,367,478 301,315,273

By swapping its foreign interest payment obligations forUSD obligations, IBM was no longer exposed tocurrency risk and could realize the capital gain from thedollar appreciation immediately. Moreover, The World Bank obtained CHF and GEM cheaper than it would hadit gone to the currency markets directly.

85

THE SWAP

IBMSWITZ GERMANY

WORLD BANK

USA

CHF200M

CHF CUPON

DEM300M

DEM CUPON

DEM CUPON

USD CUPON

USD CUPON

IBM PAY RECEIVE RECEIVEDate USD CHF DEM3.30.82 20,066,667 12,375,000 30,000,0003.30.83 33,600,000 12,375,000 30,000,0003.30.84 33,600,000 12,375,000 30,000,0003.30.85 33,600,000 12,375,000 30,000,0003.30.86 243,600,000 212,375,000 330,000,000

CHF CUPON

USD CAPITAL

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 A

F1

PROJECT OF F2

COUNTRY B

F2

PROJECT OF F1

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 CHILE BRAZIL

CH1 $12% R16%

BR2 $15% R17%

91

DIRECT SWAP FIXED FOR FIXED

CHILE

CH1 BORROWS CLP2.5B AND

DEPOSITS IT IN BR2’S ACCOUNT IN SANTIAGO

BRAZIL

BR2 BORROWS BR10M AND DEPOSITS IT IN CH1’S ACCOUNT

IN SAO PAULO

CH1 BR2

CLP12% BR17%

BR15%

CLP12%

CH1 pays BR15%; BR2 pays CLP12% + BR2%

92

INDIRECT SWAP FIXED FOR FIXED

CHILE

CH1 BORROWS CLP2.5B AND

DEPOSITS IT IN BR2’S ACCOUNT IN SANTIAGO

BRAZIL

BR2 BORROWS BR10M AND DEPOSITS IT IN CH1’S ACCOUNT

IN SAO PAULO

CH1 BR2

CLP12% BR17%

BR15.50% CLP12%

SWAP DEALERBR17%CLP14.50%

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

intermediary’s 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 SwapsEXAMPLE: 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 aSeven 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

ITALY

F1 BORROWS EUR50M AND

DEPOSITS IT IN F2’s ACCOUNT IN MILAN

U.S.A

F2 DEPOSITS USD60M IN F1’S ACCOUNT IN

NEW YORK CITY

F1 F2

EUR11.5%

USD9.35%

EUR11.5%

At maturity, the original principals are exchanged to terminate the swap.

USD9.35%

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 party’s 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

ITALY

F1 BORROWS EUR50M AND DEPOSITS IT IN

F2’s ACCOUNT IN MILAN

U.S.A

F2 DEPOSITS USD60M IN F1’S ACCOUNT IN

NEW YORK CITY

F1 F2

EUR11.5%

USD9.55%

EUR11.25%

At maturity, the original principals are exchanged.

USD9.55%

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% GBPLIBOR + 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 GB2’s account in Mexico D.F. While GB2 borrows GBP5,000,000 in Great Britain and deposits it in MX1’s account in London.

101

DIRECT SWAP FIXED FOR FLOATING

MEXICO

MX1 BORROWS MXP75M AND

DEPOSITS IT IN GB2’S ACCOUNT IN

MEXICO D.F.

ENGLAND

GB2 BORROWS GBP5,000,000 AND

DEPOSITS IT IN MX1’S ACCOUNT IN LONDON,

MX1 GB2

MXP15% GBP L + 1%

GBP L + 1%

MXP15%

MX1 pays GBP L+1%; 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 VALUATIONUnder 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.

V

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:

.EUR352,500

)2

1(

100

5.875[EUR12M]

107

Therefore, the present value of the Interest rate payments in USD plus principal is:

718.USD10,016,

EUR][USD.8333/

000(.8922)EUR12,000,

.8922].9190

.9456[.9699EUR352,500

)]S(USD/EUR[B Flows)PV(Cash EURUSD

The coupon payment of the semi-annual interest payments in USD is:

.USD187,500)2

1(

100

3.75[USD10M]

108

Therefore, the present value of the interest ratepayments in USD plus principal is:

31.USD9,946,9

000(.9249)USD10,000,

.8249].9467

.9667[.9840USD187,500

BUSD

109

The value of the foreign currency swap is:

USD48,683.

81USD9,965,6-364USD10,014,

B-Flow)PV(Cash USDUSD

110

3.COMMODITY SWAPSThe 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 SwapConsider 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

Refinery Swap Dealer

Oil Daily Spot Price

USD24.20/bbl = USD726,000

Average Spot Price

The commodity: 30,000 Barrels(1,000/day).

114

SPOT OIL MARKET

Italian Refinery

Swap Dealer

A

OIL Daily spot price

USD726,000

Average spot price

Swap Dealer

B

USD726,000/1.2

=EUR648,214

USD726,000

115

Valuation of Commodity of SwapsIn 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) = PV0{V(t1, t1)}

= PV0[S(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 PV0[S(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:PV0[S(t1)] - F(0, t1)B(0, t1).

118

Like any forward, the forward price is setsuch that no cash is exchanged when the contract is written. This implies that the value of the forward contract, wheninitiated, is zero. That is:

PV0[S(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:

n

1jpjj0 .)Nt(0,P(Fixed)]B)t[F(0,V

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 – 11:45AM

From BP’s 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

DATE SPOT FUTURES

April 12 CONTRACTS: Long SEP NYMEX

Buy from BM. Futures.

SELL TO SST F4,12; SEP = $6.87.August 12

(i) 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

A PARTIAL SUMMARY of BP POSITION

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

BP SWAP DEALER F8,12,SEP – USD.09

S1

A FLOATING FOR FLOATING SWAP

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 FLOWSpot: 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

BM SST

NYMEX

BP

F8.12,SEP - .09 S1

S1F4,12;SEP - .06

NG NG

LONGF4,12;SEP

SHORTF8.12,SEP

FUTURES

SPOT:

SWAP:

MARKET

4. BASIS SWAPSA 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.

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 HEDGER’S SELLING PRICE:

F0,T + Bk,T + B0,T - Bk,T = F0,T + B0,T = F0,T + S0 - F0,T

= S0 .

SHORT HEDGER

SWAP DEALER

B0,T

Bk,T

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 HEDGER’S PURCHASING PRICE:

F0,T + Bk,T + B0,T - Bk,T = F0,T + B0,T = F0,T + S0 - F0,T

= S0 .

LONG HEDGER

SWAP DEALER

B0,T

Bk,T

1. PRICE RISK

2. BASIS RISK

3. NO RISK AT ALL. THE CASH FLOW IS:

THE CURRENT CASH PRICE!

BASIS SWAP

FUTURES HEDGING

BASIS SWAP

NYMEXBuy NG at“Screen - 10” FUSD6.60

USD6.50

GAS

POWER PLANT

GAS PRODUCER

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.

SWAP DEALER

- 10

S - F

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 LIBOR+25pbs LIBORFIXED 8%(=MXP37.181.898) 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

MEXICAN FIRM

OIL PRODUCERS

SWAP DEALERCOMMODITY

SWAP DEALERINTEREST RATES

SWAP DEALERFORX

150,000bbls USD S

USD ave(S)

USD26/bbl Total USD3.9M

150,000bbls

USD3.9M

USD LIBOR

USD156M =

USD3.9M/0.025

NPV=3.9/(1.025)t

= USD60,797,733

EXCHANGE: USD1=MXP10

=MXP607,977,330

MXP607,977,330=C/(1.02)t

C = MXP37,181,898

MXP37,181,898 USD LIBOR

USD156MMXP1,859,094,907=

MXP37,181,898/0.02

The swap: Quarterly payments for the next 5 years