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SWAPS
Swaps are a form of derivative instruments. Out of the variety of assets underlying swaps we
will cover:
INTEREST RATES SWAPS,
CURRENCY SWAPS, and
COMMODITY SWAPS.
We will also see that a combination of hedging with
futures and swapping the basis, leads to risk-free strategies.
2
SWAPS
A SWAP is a contractual arrangement between two
parties for an exchange of cash flows.
The amounts of money involved are based on a NOTIONAL AMOUNT OF
CAPITALNotional as in conceptual
3
It follows that in a swapwe have:
1. Two parties
2. A notional amount
3. Cash flows
4. A payment schedule
5. An agreement as to how to resolve
problems
4
1. Two parties:
The two parties in a swap are sometimes 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
intermediary.
5
2. The NOTIONAL AMOUNT is
the basis for the determination of the cash flows. It is almost never
exchanged by the parties. For example:
$100,000,000
£50,000,000
50,000 barrels of crude oil
6
3. The cash flowsmay be of two types:
a fixed cash flow or
a floating cash flow.
Fixed interest rate vs.
Floating interest rate
Fixed price Vs.
Market price
7
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)(Lt+30bps);
Floating.The price, fixed or market,multiply the commodity
notional amount in order to determine the cash flows.
Ex: (100,000bbls)($24,75) = $2,475,000;
Fixed.(100,000bbls)(St );
Floating.
8
4. The payments
are always net.
The agreement determines the cash
flows timing as annual, semiannual or
monthly, etc. Every payment is the net of the two cash flows
9
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.
10
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.
11
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 $35million. The swap is for five years.
Two weeks later, the six-month LIBOR rate is 6.45% per annum.
12
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:
.74.$1,254,802 100
19.7
365
(182)0$35,000,00
100
RateFixed
Period
in Days
amount
Notional
This calculation is based on the assumption that the payment is
every 182 days.
13
The floating side is quoted as a money market yield
basis. Therefore, the first payment is:
.$1,194,375 100
.30)45.6(
360
(182)0$35,000,00
100
RateFloating
Period
in Days
amount
Notional
Other future payments will be determined every 6 months by
the six-month LIBOR at that time.
14
As in any SWAP, the payments
are netted.
In this case, the first payment is:Party A pays Party B the net
difference:
$1,254,802.74 - $1,194,375.00
= $60,427.74.
Party A Party B
FIXED 7.19%
FLOATING
LIBOR 30 bps
15
This example illustrates 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, principal 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.
16
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.
17
Example: A FIXED FOR FLOATING SWAP
Two firms need financing for projects and are facing 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%).
18
Now, suppose that the firms decide to enter a FIXED for FLOATING swap based on the notional of
$10.000.000.
The payments:
Annual payments to be made on the first business day in March for
the next five years.
19
The SWAP always begins
with each party borrowing capital in the market in which it has a
RELATIVE ADVANTAGE.
Thus, F1 borrows S $10,000,000
in the market for floating rates, I.e., for LIBOR + 2% for 5 years.
F2 borrows $10,000,000
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
20
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.
21
Two ways to negotiate the contract:
1. Direct negotiations between the two parties.
2. Indirect negotiations between the two parties.
In this case each party separately negotiates with
an intermediary party.
22
Usually,
The intermediary is a financial institution – a
swap dealer - who possesses a portfolio of
swaps.
The intermediary charges both parties commission
for its services and also as a compensation for the risk it assumes by entering the
two swaps
23
FIXED FOR FLOATING SWAP
1. A DIRECT SWAP:
FIRM FIXED RATE FLOATING RATE
F1 15% LIBOR + 2%
F2 12% LIBOR + 1%
notional: $10M
F2 F112%
LIBORLIBOR+2%
12%
The result of the swap:
F1 pays fixed 14%, better than 15%.
F2 pays floating LIBOR, better than LIBOR + 1%
24
2. AN INDIRECT SWAP
FIRM FIXED RATE FLOATING RATE
F1 15% LIBOR + 2%
F2 12% LIBOR + 1%
The notional amount: $10M
F2 F1I
12%
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 Intermediary gains 50 bps = $50,000.
25
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 intermediaries to be happy with 10 basis points. In the present example, another
possible swap arrangement is:
F2 F1IL+5bp L
12% 12%+5bp
Clearly, there exist many other possible swaps between the two
firms in this example.
L+2%12%
26
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.
27
EXAMPLE: A RISK MANAGEMENT SWAP
MARKET
BONDS
BANK
12%
10%
FIRM A
BORROWS AT A FIXED RATE FOR 5 YEARS
FL1
COUNTERPARTY
A FL2
LOAN
LOAN
FL1 = Floating rate 1.
FL2 = Floating rate 2.
28
THE BANK’S CASH FLOW:
12% - FLOATING1 + FLOATING2 – 10%
= 2% + SPREAD
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.
29
EXAMPLE: A RISK MANAGEMENT SWAP
MARKET
SHORT TERM BOND
BANK
12%
10%
FL1
COUNETRPARTY a
FL2
COUNTERPARTY b
FL1
FL2
FIRM A
30
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
RISK-FREE RATE!
31
VALUATION OF 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, however, they are only liquid out to about four years, thereby somewhat limiting the use of this method.
32
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.
33
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.
34
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.
35
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.
36
NOTATIONS: Let the swap have a tenor of m months (m/12 years). The swap is to be priced off three-month Eurodollar futures, thus, pricing requires n sequential futures series; n = m/3 or, equivalently, m = 3n.Step 1: Use the futures Euro strip to Calculate the implied effective annual LIBOR for the full tenor of the swap:
futures.r Eurodollath- tby the
covered days ofnumber actual the
denotes N(t) ;N(t)
360k :where
1,)]360
N(t)(r [1r
kn
1t1),3(t)-3(t0,3n
37
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
38
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:
39
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
SEP91 95.94 4.06 3,6 91
DEC9195.69 4.31 6,9 90
MAR92 95.49 4.51 9,12 92
JUN92 95.18 4.82 12,15 92
SEP92 94.92 5.08 15,18 91
DEC9294.64 5.36 18,21 91
MAR93 94.52 5.48 21,24 92
JUN93 94.36 5.64 24,27 92
SEP93 94.26 5.74 27,30 91
DEC9394.11 5.89 30,33 90
MAR94 94.10 5.90 33,36 92
JUN94 94.02 5.98 36,39 92
SEP94 93.95 6.05 39,42 91
40
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 91 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.
41
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.
42
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:
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
43
Step 2 and 3:
basis. bondquarterly a on 4.33%
1}(4)]360
3654340.{[1
1}(f)]360
365r{[1 SC
:as rewritten be can FRE(0,3n),
of onsubstituti 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.
44
In this swap, four net payments will take place during the one year tenure of the swap depending the three-month LIBOR realizations.
This completes the example. 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.
7.19%
LIBOR + 30
Client Swap dealer
4.33%+s
FLOATING
3-M LIBOR
FIXED
45
Client Swap dealer
4.35%+s
FLOATING
6-M LIBOR
FIXED
basis. bond
semiannuala on 4.35%, SC
);2)](1)360
365(.0434[1 SC 2
1
46
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:
47
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
Step 2: The Fixed Rate Equivalent effective annual rate on a bond basis is:
FRE = (5.17%)(365/360) = 5.24%.
48
Finally,Step 3: The equivalent semiannual
Swap Coupon is calculated:
SC = [(1.0524).5 – 1](2) = 5.17%.
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.
49
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.
50
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
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. The data are:
B(0,T)=PV of $1.00 paid at T.L(0,T)=PV of 1Euro$ paid at T. These prices are respectively, derived from the Treasury and Eurodollar term structures.
51
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
52
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.
53
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
54
The value of the swap to thefinancial 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.
55
SWAP VALUATION:The general formula
To generalize the above example, we replace algebraic symbols for the numbers.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:
n
1j
jjPFIXED ]}.
365
k][
100
R)[T{B(0,N(0)V
56
Arriving at the value of the floatingrate payments requires more analysis.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
57
The total value of the floating rate payments at date T1 is:
).T,L(TNN 360
kλN)(TV
n1PP
1P1FLOATING
).T L(0, )T)L(0,T,L(T
because trueholds This
).TL(0,N-
)TL(0,1360
kλN (0)V
:)(TV
n1n1
nP
11
PFLOATING
1FLOATING
The value of the floating rate payments at date 0 is the PV of:
58
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
)].T L(0,-[1N (0)V
).TL(0,N-
)TL(0,1360
Tλ(0)N (0)V
nPFLOATING
nP
11
PFLOATING
59
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
Notice that this value can be positive ,zero, or negative depending upon current rates.
This conclude the analysis of
plain vanilla swap valuation.
60
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
61
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 ValuationThe example below illustrates the
valuation of an interest rate par swap.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:
B(0,T)=PV of $1.00 paid at T.L(0,T)=PV of 1Euro$ paid at T. These prices are respectively, derived from the Treasury and Eurodollar term structures.
62
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 = .1316/1.8421
R = 7.14% per annum.
63
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
Germany, exchange it to USD and repay it later, exchanging USD into
German marks.
Currency swaps are basically, interest rate swaps accross countries
64
Case Study of a currency swap:
IBM and The World Bank
A famous example of an early currencySwap took place between IBM an the
World Bank in August 1981, with Salomon
BrothersAs the intermediary.The complete details of the swap have
neverbeen published in full.The following description follows a paperpublished by D.R. Bock in Swap Finance, Euromoney Publications.
65
In the mid 1970s, IBM had issued bonds inGerman marks, DEM, and Swiss francs,CHF. The bonds maturity date was March30, 1986. The issued amount of the CHFbond was CHF200 million, with a couponrate of 6 3/16% per annum. The issuedamount of the DEM bond was DEM300million with a coupon rate of 10% perannum.During 1981 the USD appreciated sharplyagainst both currencies. The DEM, for example, fell in value from $.5181/DEM inMarch 1980 to $.3968/DEM in August 1981.Thus, coupon payments of DEM100 hadfallen in USD cost from $51.81 to $39.68. 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.
66
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 Bankon August 11, 1981, settling on August25, 1981. August 25, 1981 became thesettlement date for the swap. The firstannual payment under the swap wasdetermined to be on March 30, 1982 –
thenext coupon date on IBM's bonds. I.e.,215 days (rather than 360) from the swapstarting date.
67
The swap was intermediated by Solomon Brothers.
The first step was to calculate the value of
the CHF and DEM cash flows. At thattime, the annual yields on similar bondswere at 8% and 11%, respectively.Theinitial period of 215-day meant that thediscount factors were calculated asfollows:
,
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.
68
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.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.
69
The terms of the swap were agreed uponon August 11, 1981. Thus, The World Bankwould have been left exposed to currencyrisk for two weeks until August 25. TheWorld Bank decided to hedge the abovederived NPV amounts with 14-dayscurrency forwards.Assuming that these forwards were at$.45872/CHF and $.390625/DEM, The
WorldBank needed a total amount of
$205,485,000;$87,783,247 to buy the CHF and$117,701,753 to buy the DEM.$205,485,000.
This amount needed to be divided up to the
various payments. The only problem wasthat the first coupon payment was for 215days, while the other payments were
basedon a period of 360 days.
70
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:
$205,485,000/0.9785 = $210,000,000.
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:
$210,000,000(.16)[215/360] = $20,066,667.
71
The cash flows are summarized in thefollowing 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 paymentobligations for USD obligations, IBM wasno longer exposed to currency risk andcould realize the capital gain from thedollar appreciation immediately.
Moreover,The World Bank obtained Swiss francsand German marks cheaper than it wouldhad it gone to the currency marketsdirectly.
72
Foreign Currency Swaps
EXAMPLE: a “plain vanilla”
foreign currency swap. Counterparty F1 has issued bonds with face value of £50M with a annual coupon of 11.5%, paid semi-annually and maturity of seven years.
Counterparty F1 would prefer to have dollars and to be making interest payments in dollars. Thus counterparty F1 enters into a foreign currency swap with counterparty F2 - usually a financial institution. In the first phase of the swap, party F1 exchanges the principal amount of £50M with party F2 and, in return, receives principal worth $72.5M. Usually, this exchange is done in the current exchange rate, i.e., S = $1.45/£ in this case.
73
The swap agreement is as follows:Party F1 agrees to make to counterparty F2semi – annual interest rate payments at therate of 9.35% per annum based on the Dollar denominated principal for a sevenYear period.In return, counterparty F1 receives fromparty F2 a semi-annual interest rate at theannual rate of 11.5%, based on the sterlingdenominated principal for a seven year period.The swap terminates at the maturity sevenyears later, when the principals are again exchanged:party F1 receives the principal worth £50M and counterparty F2 receives the principal Amount of $72.5M.
74
DIRECT SWAP FIXED FOR FIXED
Great Britain
F1 BORROWS £50M AND
DEPOSITS IT IN COUNTERPARTY F2’s ACCOUNT IN
LONDON
U.S.A
F2 DEPOSITS $72.5M IN
COUNTERPARTYF1’S ACCOUNT IN NEW YORK
CITY
F1 F2
£11.5%
$9.35%
£11.5%
At maturity, the original principals are exchanged to terminate the swap.
75
By entering into the foreign currency swap, counterparty F1 has successfully transferred its sterling liability into a dollar liability.
In this case, party F2 payments to party F1 were based on the the same rate of party’s F1 payments in Great Britain - £11.5%. Thus, party F1 was able to exactly offset the sterling interest rate payments.
This is not necessarily always the case. It is quite possible that the interest rate payments counterparty F1 receives from counterparty F2 only partially offset the sterling expense.
In the same example, the situation may change to:
76
DIRECT SWAP FIXED FOR FIXED
Great Britain
F1 BORROWS £50M AND
DEPOSITS IT IN COUNTERPARTY F2’s ACCOUNT IN
LONDON
U.S.A
F2 DEPOSITS $72.5M IN
COUNTERPARTYF1’S ACCOUNT IN NEW YORK
CITY
F1 F2
£11.5%
$9.55%
£11.25%
At maturity, the original principals are exchanged to terminate the swap.
77
THE ANALYSIS OF
CURRENCY SWAPS
F1 IN COUNTRY A LOOKS FOR FINANCING IN COUNTRY B
AT THE SAME TIME
F2 IN COUNTRY B, LOOKS FOR FINANCING IN COUNTRY A
COUNTRY A
F1
PROJECT OF
F2
COUNTRY B
F2
PROJECT OF
F1
78
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.
79
CURRENCY SWAP FIXED FOR FIXED
CP = Chilean Peso
R = 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:
80
FIRM CHILE BRAZIL
CH1 $12% R16%
BR2 $15% R17%
With these rates, CH1 has absolute advantage in both markets but, comparative advantage in Chile only.
CH1 borrows in Chile in Chilean Pesos and BR2 borrows in Brazil in Reals. The swap begins with the interchange of the principal amounts borrowed 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.
81
ASSUME THAT THE CURRENT EXCHANGE RATE IS:
R1 = CP250
ASSUME THAT CH1 NEEDS R10.000.000 FOR ITS PROJECT IN
BRAZIL AND THAT BR2 NEEDS EXACTLY CP2,5B FOR ITS
PROJECT IN CHILE.
AGAIN:
FIRM CHILE BRAZIL
CH1 $12% R16%
BR2 $15% R17%
82
DIRECT SWAP FIXED FOR FIXED
CHILE
CH1 BORROWS CP2.5B AND
DEPOSITS IT IN BR2’S
ACCOUNT IN SANTIAGO
BRAZIL
BR2 BORROWS R10M AND
DEPOSITS IT IN CH1’S ACCOUNT IN SAO PAULO
CH1 BR2
$12% R17%
R15%
$12%
CH1 pays R15%; BR2 pays CP12% + R2%
83
INDIRECT SWAP FIXED FOR FIXED
CHILE
CH1 BORROWS CP2.5B AND
DEPOSITS IT IN BR2’S
ACCOUNT IN SANTIAGO
BRAZIL
BR2 BORROWS R10M AND
DEPOSITS IT IN CH1’S ACCOUNT IN SAO PAULO
CH1 BR2
$12% R17%
R15.50% $12%
INTERMEDIARY
R17%$14.50%
84
THE CASH FLOWS:
CH1: PAYS R15.50%
BR2: PAYS CP14.50%
THE INTERMEDIARY REVENUE:
CP2.50 – R1.50%
CP2,5B(0.025) – R10M(0.015)(250)
= CP62,500,000 - CP37,500,000 = CP25,000,000
Notice: In this case, CH1 saves 0.25% and BR2 saves 0.25%, while the
intermediary bears the exchange rate risk. If the Chilean Peso depreciates against the Real the intermediary’s
revenue declines. When the exchange rate reaches CP466,67/R the
intermediary gain is zero. If the Chilean Peso continues to depreciate the
intermediary loses money on the deal.
85
FIXED FOR FLOATING
CURRENCY SWAP
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.
86
DIRECT SWAP FIXED FOR FLOATING
INTEREST RATES
MEXICO GREAT BRITAIN
MX1 MP15% £LIBOR + 3%
GB2 MP18% £LIBOR + 1%
ASSUME: The current exchange rate is: £1 = MP15.
MX1 needs £5.000.000 in England and GB2 needs MP75.000.000 in Mexico.
THUS:
MX1 borrows MP75m in Mexico and deposits it in GB2’s account in Mexico
D.F., Mexico, While GB2 borrows £5,000,000 in Great Britain and
deposits it in MX1’s account in London, Great Britain.
87
DIRECT SWAP FIXED FOR FLOATING
MEXICO
MX1 BORROWS MP75M AND
DEPOSITS IT IN GB2’S
ACCOUNT IN MEXICO D.F.,
MEXICO.
ENGLAND
GB2 BORROWS £5,000,000 AND DEPOSITS IT IN
MX1’S ACCOUNT IN LONDON,
GREAT BRITAIN
MX1 GB2
MP15% £L + 1%
£L + 1%
MP15%
MX1 pays £L+1%; GB2 pays MP15%
88
DIRECT SWAP FIXED FOR FLOATING
AGAIN: MX1 pays £L+ 1%;
GB2 pays MP15%.
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 £L+ 1%, a better rate than £LIBOR + 3%, the rate it would have paid had it borrowed
directly in the floating rate market in Great Britain.
GB2 pays MP15% fixed, which is better than the MP18% it would have paid had
it borrowed directly in Mexico.
89
A plain vanilla CURRENCY SWAPS VALUATION
Under the terms of a swap, party A receives French francs (FF) interest rate payments and making dollar ($) interest payments. Let us measure the amount in . Also, use the following notation:BFF = PV of the payments in FF from party B, including the principal payment at maturity.B$ = PV of the payments in $ from party A, including the principal payment at maturity. S0(FF/$) = the current exchange rate.
Then, the value of the swap to counterparty A in terms of sterling is:
VFF = BFF - S0(FF/$)B$.
V
90
Note that the value of the swap depends upon the shape of the domestic term structure of interest rates and the foreign term structure of interest rates.EXAMPLE: A ‘PLAIN VANILLA’ CURRENCY SWAP VALUATION
Consider a financial institution that entersinto a two-year foreign currency swap for which the institution receives 5.875% per annum semiannually in French francs (FF) and pays 3.75% per annum semi-annuallyin U.S. dollars ($). The principals in the two currencies are FF58.5M $10M, reflecting the current exchange rate: S0(FF/$) = 5.85.
Information about the U.S. and French term structures of interest rates is given in following table:
91
Domestic and Foreign Term Structure*
Maturity Price of a zero coupon Bond Months $ FF 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 French Francs is:
50.1,718,437. FF
)2
1(
100
5.875[FF58.5M]
92
Therefore, the present value of theinterest rate payments in U.S Dollars plus principal is:
4.$10,014,36
][$.1709/FF
00(.8922)FF58,500,0
.8922].9190
.94567.59[.9699FF1,718,43
S($/FF) B Flows)PV(Cash FF$
The coupon payment of the semi-annual interest payments in U.S Dollars is:
187,500. $)2
1(
100
3.75[$10M]
93
Therefore, the present value of theinterest rate payments in U.S Dollars plusprincipal is:
.$9,965,681
0(.9249)$10,000,00
.8249].9467
.96679840$187,500[.
B$
Therefore, the
value of the foreign currency swap
is:
$48,683.
9,965,681-4$10,014,36
B- Flow)PV(Cash $$
94
3.COMMODITY SWAPS
The huge success of domestic interest rate swaps and foreign currency swaps
lead investors and firms to look for other markets for swaps. In the 1980s and the 1990s swaps began trading on
a large range of underlying assets. Among these are: Commodities, stocks, stock indexes, bonds and other types of
debt instruments.
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.
95
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.Party B pays party A an agreed upon
floating price for a given 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.
96
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 $24.20 per barrel.The refinery agrees to make monthly payments to the swap dealer at a fixed rate of $24.20 per barrel.The swap dealer agrees to pay the refinery the average daily price for oil during the preceding month.The notional principal is 30,000 barrels.
97
Spot oil market
Refinery
Swap Deale
r
Oil Spot Price
$24.20/bbl
Average Spot Price
The commodity: 30,000 bbls.
98
Note that in the swap no exchange of the notional commodity takes place between the counterparties. The refinery has reduced its exposure to the volatile oil prices in the markets. It still, however, bear some risk. This is because there may be a difference between the spot price and the average spot price. The refinery is still buying oil and paying the spot price, and from the swap dealer it receives the last month's average spot price. It also pays to the swap dealer $24.20 per barrel over the life of the contract. Therefore, the spread between the spot and last month average prices presents some risk to the refinery.
99
A NATURAL(NG) SWAP:
FIXED FOR FLOATING.
MC – a marketing firm buys NG from a producer for the fixed price of
$9.50/UNIT (1,000 cubic feet). At the same time MC finds an end user and sells the NG. The end user insists on paying a floating market price index.
The index is published daily according NG prices in different locations.
MC’s risk is that the index falls below $9.50.
MC enters a FIXED FOR FLOATING swap in which it pays the swap dealer the
index and recieves $9.55/tcf
The notional amount of NG is equal to the amount purchased and sold by MC.
100
A FISED-FOR-FLOATINGNATURAL GAS SWAP
PRODUCER MC END USER
SWAP DEALER
$9.55 INDEX
INDEX$9.50
Gas Gas
MC’s cash flow is:
- $9.50 + Index + $9.55 – Index
= $0.05/UNIT
101
FLOATING FOR FLOATING NATURAL GAS SWAP
There are several different energy indexes for various energy
commodities. Thus, it is very possible that MC will buy the
natural gas for one index and sell it to the end user for another
index. In these cases, both cash flows are based on floating rates
and MC faces the exposure of the floating spread. MC may be able to enter a swap and fix a positive
spread for its revenues.
102
FLOATING-FOR-FLOATING NATURAL GAS SWAP
producer MC USER
Swap Dealer
INDEX1 INDEX2 - $0.08
INDEX2INDEX1
Gas Gas
In this case MC’s cash flow is:
(Index2) – (Index1)
+ (Index1) – ( Index2 - $0.08)
= $0.08/UNIT.
103
Valuation of Commodity of Swaps
The value of a “plain vanilla” commodity swap.
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.
104
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 thecurrent spot price. In practice, however, there are carrying costs and convenience yields.
105
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).
106
Like any forward, the forward price is set such that no cash is exchanged
when the contract is written. This implies
thatthe value of the forward contract, when initiated, is zero. That is:
PV0[S(t1)] = F(0, t1)B(0, t1).
Using this expression, the value at date
0of the first swap payment is:
V(0,tl) = [F(0,t1) - P(fixed,t1)]B(0, tl)NP.
107
Repeating this argument for the remaining payments, it can be shown that the
value of the commodity swapat 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.
108
FINAL EXAMPLE:
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 swapping the
remaining spread. First, let us define:
The following two indexes:
1. L3D - LAST THREE DAYS
A weighted average of NYMEX NG futures prices during the last three trading days of the contract.
2. IF - INSIDE FERC
A weighted average of NG spot prices at various places.
109
April 12 – 11:45AM
From BP’s derivative trading room
1. The 1st call:
BP agrees to buy NG from BM in August for IF.
2. The 2nd call:
BP hedges the NG purchase going long NYMEX’ August NG futures.
3. The 3rd call: BP finds a buyer for the gas - SST. But, SST
negotiates the purchase price to be at some discount off the current August NYMEX NG
futures. Let $X be the discount amount. $X is left unknown for
now.
110
DATE SPOT FUTURES
April 12 Buy from BM. Long August NYMEX
Sell to SST. Futures.
F4,12; aug = $3.87.
August 12 (i) Buy NG from BM Short August NYMEX
S1 = IF . Futures.
(ii) Sell NG to SST for Faug; aug = L3D
S2 = F4, 12; aug – $X
PARTIAL CASH FLOW:
(F4,12; aug – $X) – IF + L3D - F4,12; aug
= L3D – $X – IF.
A PARTIAL SUMMARY
111
How can BM eliminate the spread risk?
BP decides to enter a spread swap.
Clearly, this is a floating for floating swap.
4.The 4th call: BP enters a swap whereby
BP pays the Swap dealerL3D – $.09 and receives
IF from the Swap dealer.
The swap is described as follows:
112
BP SWAP DEALER L3D - $.09
IF
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.
113
SUMMARY OF CASH FLOWS
MARKET CASH FLOWSpot: F4, 12; AUG - $X - IF Futures: + L3D - F4, 12; AUG
Swap: + IF - (L3D – $.09) TOTAL = $.09 - $X. BP decides to make 3 cents per unit. Solving $.03 = $.09 - $X for $X yields: $X = $.06.
5. The 5th call BP calls SST and both agree that SST buys the NG from BP in August for today’s NYMEX - $.03. I.e., $3.87 - $.06 = $3.81.
THE END
114
THE BP EXAMPLE
SWAP DEALER
BM SST
NYMEX
BP
L3D - .09 IF
IFF4,12;AUG - $.06
NG NG
LONGF4,12;AUG
SHORTL3D
FUTURES
SPOT:
SWAP:
MARKET
4. BASIS SWAPS
A basis swap is a risk management tool that allows a hedger to eliminate the BASIS RISK associated with the 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 pays 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 =
S0 - F0,t
k Sk Fk, Bk,t = Sk - Fk,t
The selling price for the SHORT hedger is:
F0,t + Bk,t .
2. THE SWAP OF THE SHORT HEDGE:
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
Bk,t
1. THE FUTURES LONG HEDGE:
TIME CASH FUTURES BASIS 0 S0 F0,t B0 =
S0 - F0,t
k Sk Fk, Bk,t = Sk - Fk,t
The purchasing price for the LONG hedger:
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
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 gas at“Screen - 10” L3D$3.60
$3.50
GAS
POWER PLANT
GAS PRODUCER
Power plant is a long hedger.Initial basis =
–$.10. The terminal basis is S – L3D. Power plant may swap the bases: final purchasing price of:
$3.60 + S – L3D + (S - L3D - $.10)
= $3.50.
