Interest Rate & Currency Swaps
Chapter Fourteen
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Chapter Outline
•
•
•
•
•
•
•
•
•
Types of Swaps
Size of the Swap Market
The Swap Bank
Swap Market Quotations
Interest Rate Swaps
Currency Swaps
Variations of Basic Interest Rate and Currency Swaps
Risks of Interest Rate and Currency Swaps
Is the Swap Market Efficient?
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14-2
Definitions
• In a swap, two counterparties agree to a contractual
arrangement wherein they will exchange cash flows
at periodic intervals.
• There are two types of interest rate swaps.
– Single currency interest rate swap
• “Plain vanilla” fixed-for-floating swaps are often just called
interest rate swaps.
– Cross-currency interest rate swap
• This is often called a currency swap; fixed for fixed rate debt
service in two (or more) currencies.
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Size of the Swap Market
• In 2015 the notational principal of:
– Interest rate swaps was $289 trillion USD.
– Currency swaps was $22.7 trillion USD.
• The four most common currencies used to
denominate interest rate and currency swaps are the
euro, U.S. dollar, Japanese yen, and the British pound
sterling, with the fifth most common currency being
the Canadian dollar for interest rate swaps and the
Swiss franc for currency swaps.
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EXHIBIT 14.1
Size of OTC Interest Rate and Currency Swap Markets: Total
Notional Principal Outstanding Amounts in Billions of U.S.D.
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The Swap Bank
• Swap bank is a generic term to describe a financial institution
that facilitates swaps between counterparties.
• The swap bank can serve as either a broker or a dealer.
– As a broker, the swap bank matches counterparties but does
not assume any of the risks of the swap.
– As a dealer, the swap bank stands ready to accept either
side of a currency swap and then later lay off the risk, or
match it with a counterparty.
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Swap Market Quotations
• Swap banks will tailor the terms of interest rate
and currency swaps to customers’ needs.
• They also make a market in “plain vanilla”
swaps and provide quotes for these. Since the
swap banks are dealers for these swaps, there
is a bid-ask spread.
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EXHIBIT 14.2 Interest Rate Swap Quotations
Euro-€
1
2
3
4
5
6
7
8
9
10
12
15
20
25
30
year
year
year
year
year
year
year
year
year
year
year
year
year
year
year
Bid
−0.16
−0.16
−0.14
−0.08
−0.01
0.09
0.2
0.32
0.43
0.53
0.7
0.88
1.04
1.06
1.08
Ask
−0.13
−0.14
−0.10
−0.04
0.03
0.12
0.23
0.35
0.46
0.55
0.73
0.92
1.06
1.10
1.09
£ Sterling Swiss Franc
USD
JPY
Bid Ask Bid Ask Bid Ask Bid Ask
0.72 0.74 −0.73 −0.65 0.8 0.81 −0.08 −0.06
0.76 0.77 −0.73 −0.70 0.94 0.95 −0.14 −0.13
0.82 0.84 −0.72 −0.68 1.05 1.05 −0.16 −0.14
0.89 0.91 −0.67 −0.64 1.15 1.15 −0.14 −0.12
1.06–1.10
means
the1.24
swap1.24
bank
will−0.09
pay
0.97 0.99 −0.60
−0.57
−0.11
fixed-rate
euro −0.49
payments
1.06 1.08 −0.52
1.33 at
1.331.06%
−0.08 −0.04
1.16 1.17
−0.43 −0.40
1.41LIBOR
1.42 −0.04
0
against
receiving
USD
or it will
1.24 1.26 −0.35 −0.31 1.49 1.49
0
0.04
receive
fixed-rate
euro
payments
at
1.32 1.34 −0.25 −0.23 1.56 1.56 0.04 0.08
1.10%
against
1.39 1.4
−0.17 receiving
−0.14 1.62 USD
1.62 LIBOR.
0.07 0.11
1.5 25
1.52
−0.07 −0.02 NA NA 0.15 0.17
For
years.
1.61 1.63 0.06 0.11 1.87 1.87 0.28 0.31
1.67 1.68 0.18 0.23
2
2
0.42 0.45
1.66 1.67 NA NA 2.07 2.07 NA NA
1.65 1.66 0.29 0.34 2.1 2.11 0.48 0.5
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Swap Quotations: Bid-Ask Spread
1.06–1.10 means the swap bank will pay fixed-rate euro
payments at 1.06% against receiving USD LIBOR or it will
receive fixed-rate euro payments at 1.10% against paying dollar
USD LIBOR.
Firm
B
€1.10%
USD LIBOR
Swap
Bank
€1.06%
USD LIBOR
Firm
A
While most swaps are quoted against “flat” dollar LIBOR,
“off-market” swaps are available where one party pays LIBOR plus
or minus some number.
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Example of an Plain Vanilla Interest Rate Swap
Fixed
Floating
A
5%
LIBOR
B
5.50%
LIBOR + .20%
• Consider Firms A and B; each firm wants to borrow $40
million for three years.
– Firm A wants to finance an interest-rate-sensitive asset and
therefore wants to borrow at a floating rate. A has good credit
and can borrow at LIBOR.
– Firm B wants to finance an interest-rate-insensitive asset and
thus wants to borrow at a fixed rate. B has less-than-perfect
credit and can borrow fixed at 5.5%.
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Example of an Interest Rate Swap: Firm A
5.0
%
Firm 5.10% Swap
A
LIBOR Bank
Bank
X
If Firm A borrows from their bank at 5.0% fixed
and takes up the swap bank on their offer of
5.1—5.2, they can convert their fixed rate 5%
debt into a floating rate debt at LIBOR – 0.10%.
A’s all-in-cost = LIBOR – 0.10%
= 5.0% + LIBOR – 5.10%
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Example of an Interest Rate Swap: Firm B
Swap
Bank
Firm
B
LIBOR
5.20%
R
BO
LI
.2%
B’s all-in-cost = 5.40%
= –LIBOR + LIBOR + 0.20% + 5.20%
+
If Firm B borrows floating from their bank at
LIBOR + 0.20% and takes up the swap bank on
their offer of 5.1—5.2, they can convert their
floating rate debt into a fixed rate debt at 5.40%.
Bank
Y
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Example of an Interest Rate Swap: Swap Bank
Firm 5.10% Swap
A
LIBOR Bank
Firm
B
LIBOR
5.20%
The swap bank makes 10 basis points on the deal.
The swap bank’s all-in-cost:
–0.10% = –LIBOR + LIBOR – 5.20% + 5.10%
Note that a negative cost means a profit.
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Example of an Interest Rate Swap: All Parties
The notional size is $40 million.
The tenor is for 3 years.
+
A earns $40,000 per year on the swap.
.2%
Bank
X
Firm
B
LIBOR
5.20%
R
BO
LI
5.0
%
Firm 5.10% Swap
A
LIBOR Bank
B earns $40,000 per year on the swap.
The swap bank earns $40,000 per year.
Bank
Y
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Using a Swap to Transform a Liability
• Firm A has transformed a fixed rate liability into a floater.
– A is borrowing at LIBOR – .10%
– A savings of 10 bp.
Bank 5.0% Firm 5.10% Swap
A
LIBOR Bank
X
• Firm B has transformed a floating rate liability into a fixed rate
liability.
– B is borrowing at 5.40%
– A savings of 10 bp.
Swap
Bank
Firm
LIBOR + .2%
B
LIBOR
5.20%
Bank
Y
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What about the Principal?
• In our “plain vanilla” interest-only interest rate
swap, we did not mention swapping the
Notational Principal.
• It could be the case that Firm A exchanged
principal with their lender, Bank X, and Firm
B exchanged principal with their outside
lender, Bank Y.
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Cash Flows of an Interest-Only Swap: T = 0
00
,00
0
$4
0,0
00
,00
Firm
B
0,0
Bank
X
Swap
Bank
$4
0
Firm
A
Bank
Y
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Cash Flows of an Interest-Only Swap: T = 1
Assume LIBORT=0 = 3%.
The swap bank earns $40,000 per year.
Firm A saves $40,000 per year relative to
borrowing at LIBOR = 3%.
Firm B saves $40,000 per year relative to
borrowing at 5.5%.
Bank
Y
00
$2
Firm
B
$1,200,000
$2,080,000
,0
80
Bank
X
Swap
Bank
,2
$1
,00
0,0
00
Firm $2,040,000
A
$1,200,000
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Cash Flows of an Interest-Only Swap: T = 2
Assume LIBORT=1 = 4%.
$1,600,000
Swap
Bank
Firm
B
$1,600,000
$2,080,000
Firm B saves $40,000 per year relative to
borrowing at 5.5%.
$2
Bank
X
00
Firm A saves $40,000 per year relative to
borrowing at LIBOR = 4%.
0,0
,00
The swap bank earns $40,000 per year.
,68
0,0
$2,040,000
$1
00
Firm
A
Bank
Y
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Cash Flows of an Interest-Only Swap: T = 3
Assume LIBORT=2 = 5%.
$2,040,000
$2,000,000
Swap
Bank
Firm
B
$2,000,000
$2,080,000
,00
00
Firm B saves $40,000 per year relative to
borrowing at 5.5%.
Bank
Y
2,0
$4
Bank
X
0
,00
Firm A saves $40,000 per year relative to
borrowing at LIBOR = 4%.
80
2,0
The swap bank earns $40,000 per year.
$4
0
Firm
A
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Example of a Currency Swap
• Consider Firms A and B:
– Firm A is a U.S. MNC who wants to finance a euro denominated
asset in Italy, and therefore wants to borrow €40 million for 3
years. A can borrow euros at 6%.
– Firm B is a French MNC who wants to finance a dollar
denominated asset, and therefore wants to borrow $60 million for 3
years. B can borrow dollars at 8%.
$
€
A
$7%
€6%
B
$8%
€5%
• The exchange rate at inception was $1.50 = €1.00.
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Example of a Currency Swap: Swap Quotes
Suppose that the Swap Bank publishes these quotes.
The convention is to quote against U.S. dollar LIBOR.
Euro-€
Bid Ask
3 year 5.00 5.20
U.S. $
Bid
Ask
7.00
7.20
Firm A wants to finance a euro-denominated
asset in Italy and wants to borrow euros. It can
borrow euros at 6% or it can borrow euros at
A
5.2% by using a currency swap.
$
€
$7%
€6%
B $8%
€5%
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Example of a Currency Swap: Firm A
Euro-€
U.S. $
$
€
Bid
Ask
Bid
Ask
A
$7%
€6%
5.00
5.20
7.00
7.20
B
$8%
€5%
LIBOR
(The convention is to quote against U.S. dollar LIBOR.)
$7.0%
$60m
$60m
Suppose that Firm A borrows $60m
locally at $7% and then trades $60m for
€40m at spot.
Firm A then enters into 2 fixed for floating
swaps.
Firm A
€5.2%
Swap
Bank
LIBOR
€40m
Bank X
$7.0%
FOREX Market
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Example of a Currency Swap: Firm B
Euro-€
U.S. $
$
€
Bid
Ask
Bid
Ask
A
$7%
€6%
5.00
5.20
7.00
7.20
B
$8%
€5%
(The convention is to quote against U.S. dollar LIBOR.)
LIBOR
$7.2%
Firm B
€40m
LIBOR
€40m
€5%
€5.0%
$60m
Swap
Bank
FOREX Market
Bank Y
Suppose that Firm B borrows €40m
locally at €5%, then trades €40m for
$60m.
Firm B then enters into 2 fixed for
floating swaps.
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Example of a Currency Swap: Swap Bank
The swap bank earns 40bp per year (20bp in $ and 20bp in €).
€5.2%
Swap
Bank
Firm
B
€5.0%
$7.2%
The notional size is $60m.
The tenor is for 3 years.
Firm A earns 80bp per year on the swap and hedges exchange
rate risk.
Bank
X
Firm B earns 80bp per year on the swap and hedges
exchange rate risk.
.0%
$7
$7.0%
€5
.0%
Firm
A
Bank
Y
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Cash Flows of the Swaps: T = 0
0
0,0
00
,00
€4
0
0,0
00
,00
0
,00
$6
00
Foreign Exchange
Spot Market
0,0
$6
0,0
00
,00
Firm
B
€4
Bank
X
Swap
Bank
0
,00
00
0
0,0
,00
€4
00
0,0
$6
0
Firm
A
Bank
Y
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Cash Flows of the Swaps: T = 1
LIBORT=0 = 3%.
Firm
A
$1.8m
$1.8m
$4.2m
$4.32m
€2.08m
Swap
Bank
$1.8m
$1.8m
Firm B’s all-in-cost
= $4.32 or
7.2% of $60m
m
Firm A’s all-in-cost
= €2.08m or
5.2% of €40m
€2
m
The swap bank earns €80,000 + $120,000
or .002×€40m + .002×$60m per year.
.2
4
$
Bank
X
€2m
Firm
B
Bank
Y
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Cash Flows of the Swaps: T = 2
LIBORT=1 = 4%.
Firm
A
$2.4m
$2.4m
$4.2m
$4.32m
€2.08m
Swap
Bank
$2.4m
$2.4m
Firm B’s all-in-cost
= $4.32 or
7.2% of $60m
m
Firm A’s all-in-cost
= €2.08m or
5.2% of €40m
€2
m
The swap bank earns €80,000 + $120,000
or .002×€40m + .002×$60m per year.
.2
4
$
Bank
X
€2m
Firm
B
Bank
Y
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Cash Flows of the Swaps: T = 3
$3m
LIBORT=2 = 5%.
$4.2m
€2.08m
$4.32m
€2m
Firm
B
$3m
$3m
0m
$6
0m
0m
€4
$6
$6
0m
2m
€4
2m
.
4
Bank
X
Swap
Bank
€4
Firm
A
$3m
Bank
Y
Foreign Exchange Forward Market
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Equivalency of Currency Swap Debt Service
Obligations
• We can assume that IRP holds between the €5% euro rate and the
$7% dollar rate.
– This is reasonable since these rates are, respectively, the best rates available
for each counterparty who is well known in its national market.
– According to IRP:
t
(1 + i$)
St($/€) = S0($/€) ×
(1 + i€)t
$1.50×(1.07)1 $1.5286
S1($/€) =
1 =
€1.00×(1.05)
€1.00
$
€
A $7%
€6%
B $8%
€5%
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IRR
0
1
2
3
7.00%
–$60.00
$4.20
$4.20
$64.20
5.00%
–€40.00
€2.75
€2.70
€40.44
The swap bank could borrow $60m at 7% and use a set of 3
forward contracts to redenominate the bond as a 5% euro
bond.
€1.00
€1.00×(1.05)
–€40m = –$60m×
€2.75m = $4.20m ×
$1.50
$1.50×(1.07)
€1.00×(1.05)2
€2.70m = $4.20m ×
$1.50×(1.07)2
€1.00×(1.05)3
€40.44m = $64.20m ×
$1.50×(1.07)3
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IRR
0
1
2
3
7.00%
–$60.00
$3.06
$3.12
$66.67
5.00%
–€40.00
€2.00
€2.00
€42.00
The swap bank could borrow €40m at 5% and use a set of 3
forward contracts to redenominate the bond as a 7% dollar
bond.
$1.50
$1.50×(1.07)
–$60m = –€40m×
$3.06m = €2m × ×
€1.00
€1.00×(1.05)
$1.50×(1.07)2
$3.12m = €2m ××
€1.00×(1.05)2
$1.50×(1.07)3
$66.67m = €42m×
€1.00×(1.05)3
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The Quality Spread Differential
• The Quality Spread Differential (QSD) represents the potential
gains from a swap that can be shared between the
counterparties and the swap bank.
• There is no reason to presume that the gains will be shared
equally.
• The QSD is calculated as the difference between the
differences.
$
€
A
$7%
€6%
B
$8%
€5%
QSD
1%
–
–1%
= 2%
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Variations of Basic Currency and
Interest Rate Swaps
• Currency swaps:
– Fixed for fixed
– Fixed for floating
– Floating for floating
– Amortizing
• Interest rate swaps:
– Zero-for floating
– Floating for floating
• For a swap to be possible, a QSD must exist. Beyond that,
creativity is the only limit.
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Risks of Interest Rate
and Currency Swaps
• Interest rate risk
– Interest rates might move against the swap bank after it has only gotten
half of a swap on the books, or if it has an unhedged position.
• Basis risk
– Basis risk may occur if the floating rates of the two counterparties are
not pegged to the same index.
• Exchange rate risk
– In the example of a currency swap given earlier, the swap bank would
be worse off if the pound appreciated.
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Risks of Interest Rate
and Currency Swaps (continued)
• Credit risk
– This is the major risk faced by a swap dealer, the risk that a
counterparty will default on its end of the swap.
• Mismatch risk
– It’s hard to find a counterparty that wants to borrow the right amount of
money for the right amount of time.
• Sovereign risk
– The risk that a country will impose exchange rate restrictions that will
interfere with performance on the swap.
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Valuation of an Existing Swap
• A swap is a derivative security, so valuation can be
done with reference to the value of the underlying
assets.
• How to value a swap:
– Any swap’s value is the difference in the present values of
the payment streams that are incoming and outgoing.
– Plain vanilla, fixed for floating swaps get valued just like a
pair of bonds.
– Currency swaps get valued just like two nests of currency
forward contracts.
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Swap Valuation Example
• A currency swap has a remaining life of 18 months.
• It involves exchanging interest at 14% on £20 million for
interest at 10% on $30 million once a year.
• The term structure of interest rates is currently flat in both the
U.S. and the U.K. If the swap were negotiated today, the interest
rates exchanged would be $8% and £11%. All rates were quoted
with annual compounding.
• The current exchange rate is $1.65 = £1.
• What is the value of the swap (in USD) to the party paying
dollars?
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Swap Valuation Example (continued)
18
6
£2.8m
£2.8m
–$3m
–$3m
Value of the swap to the party paying dollars:
0
£2.8m
£2.8m
$1.65
$8,335,659 = (1.11)½ + (1.11)3/2 × £1
–$5,559,669 = –$3m ½ + –$3m 3/2
(1.08)
(1.08)
$2,775,990
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Second Swap Valuation Example
• Find the dollar value today to the party paying dollars
of a 7-year old swap with 3 years remaining maturity.
• The swap calls for exchanging interest only on €10m
at 5% for $15m at 3%.
– Semiannual payments, and the last payment was yesterday.
– Today’s exchange rate is $1.30/€ and the AAA rate is 2%
in the U.S. and 2.5% in the euro zone.
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Swap Valuation Example 2 (continued)
CPT
N 6
I/Y 2.5%
PV -€1,436,502.48
Find the value of the swap as the net value of a
portfolio of two bonds:
1. Long a euro-denominated bond and
2. Short a dollar-denominated bond
PMT €250,000 = (€10m × .05) /2 (semi-annual pay bond)
FV €0 (NOT €10m since this is an interest-only swap.)
dollar value = €1,436,502.48 × $1.30/€1 = $1,867,453.22
CPT
N 6
I/Y 2.0%
PV -$1,303,982.21
PMT $225,000 = ($15m × .03) /2 (semi-annual pay bond)
FV $0 (NOT $15m since this is an interest-only swap.)
The value of this swap to the party paying dollars is $563,471.02 (= $1,867,453.22 –
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Swap Market Efficiency
• Swaps offer market completeness, and that has
accounted for their existence and growth.
• Swaps assist in tailoring financing to the type desired
by a particular borrower. Since not all types of debt
instruments are available to all types of borrowers,
both counterparties can benefit (as well as the swap
dealer) through financing that is more suitable for
their asset maturity structures.
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Summary
• The basic interest rate swap is a fixed-for-floating rate swap in
which one counterparty exchanges the interest payments of a
fixed-rate debt obligation for the floating interest payments of
the other counterparty. Both debt obligations are denominated
in the same currency.
• In a currency swap, one counterparty exchanges the debt
service obligations of a bond denominated in one currency for
the debt service obligations of the other counterparty, which
are denominated in another currency.
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Inc. All rights reserved. 14-43
Summary (continued)
• A swap bank is a generic term to describe a financial institution
that facilitates the swap between counterparties. The swap bank
serves as either a broker or a dealer.
• An example of a basic interest rate swap was presented. It was
noted that a necessary condition for a swap to be feasible was the
existence of a quality spread differential between the default-risk
premiums on the fixed-rate and floating-rate interest rates of the
two counterparties.
• Pricing an interest rate swap after inception was illustrated. It was
shown that after inception, the value of an interest rate swap to a
counterparty should be the difference in the present values of the
payment streams the counterparty will receive and pay on the
notional principal.
Copyright © 2018 by the McGraw-Hill Companies,
Inc. All rights reserved. 14-44
Summary (concluded)
• A detailed example of a basic currency swap was presented. It
was shown that the debt service obligations of the counterparties
in a currency swap are effectively
equivalent to one another in cost. Nominal differences can be
explained by the set of international parity relationships.
• Pricing a currency swap after inception was illustrated. It was
shown that after inception, the value of a currency swap to a
counterparty should be the difference in the
present values of the payment stream the counterparty will
receive in one currency and pay in the other currency, converted
to one or the other currency denomination.
Copyright © 2018 by the McGraw-Hill Companies,
Inc. All rights reserved. 14-45