Chapter 13
Swaps and Interest
Rate Options
1
© 2004 South-Western Publishing
Outline
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Introduction
Interest rate swaps
Foreign currency swaps
Circus swap
Interest rate options
Introduction
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Both swaps and interest rate options are
relatively new, but very large
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In mid-2000, there was over $60 trillion
outstanding in interest rate swaps, foreign
currency swaps, and other interest rate options
Interest Rate Swaps
Introduction
 Immunizing with interest rate swaps
 Exploiting comparative advantage in
the credit market
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Introduction
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Popular with bankers, corporate
treasurers, and portfolio managers
who need to manage interest rate risk
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A swap enables you to alter the level
of risk without disrupting the
underlying portfolio
Introduction (cont’d)
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The most common type of interest rate swap
is the fixed for floating rate swap
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One party makes a fixed interest rate payment to
another party making a floating interest rate
payment
Only the net payment is made (difference check)
The firm paying the floating rate is the swap seller
The firm paying the fixed rate is the swap buyer
Introduction (cont’d)
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Typically, the floating interest rate is linked
to a market rate such as LIBOR or T-bill
rates
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The swap market is standardized partly by
the International Swaps and Derivatives
Association (ISDA)
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ISDA provisions are master agreements
Introduction (cont’d)
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A plain vanilla swap refers to a standard
contract with no unusual features or bells
and whistles
The swap facilitator will find a counterparty
to a desired swap for a fee or take the other
side
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A facilitator acting as an agent is a swap broker
A swap facilitator taking the other side is a swap
dealer (swap bank)
Introduction (cont’d)
Plain Vanilla Swap Example
A large firm pays a fixed interest rate to its bondholders,
while a smaller firm pays a floating interest rate to its
bondholders.
The two firms could engage in a swap transaction which
results in the larger firm paying floating interest rates to the
smaller firm, and the smaller firm paying fixed interest rates
to the larger firm.
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Introduction (cont’d)
Plain Vanilla Swap Example (cont’d)
LIBOR – 50 bp
Big Firm
8.05%
Bondholders
10
8.05%
Smaller
Firm
LIBOR +100 bp
Bondholders
Introduction (cont’d)
Plain Vanilla Swap Example (cont’d)
A facilitator might act as an agent in the transaction and
charge a 15 bp fee for the service.
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Introduction (cont’d)
Plain Vanilla Swap Example (cont’d)
LIBOR -50 bp
Big Firm
8.05%
Bondholders
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8.05%
LIBOR -50 bp
Facilitator
8.20%
Smaller
Firm
LIBOR +100 bp
Bondholders
Introduction (cont’d)
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The swap price is the fixed rate that the two
parties agree upon
The tenor is the term of the swap
The notional value determines the size of
the interest rate payments
Counterparty risk refers to the risk that one
party to the swap will not honor its part of
the agreement
Immunizing With Interest Rate
Swaps
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Interest rate swaps can be used by
corporate treasurers to adjust their
exposure to interest rate risk
The duration gap is:
D gap
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Total Liabilitie s
 D asset 
 D liabilities
Total assets
Immunizing With Interest Rate
Swaps (cont’d)
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A positive duration gap means a bank’s net
worth will suffer if interest rates rise
–
The treasurer may choose to move the duration
gap to zero
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This could be accomplished by selling some of the
bank’s loans and holding cash equivalent securities
instead
Immunizing With Interest Rate
Swaps (cont’d)
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Using the bank’s balance sheet, we can
algebraically solve for the proportion of the
firm’s assets to be held in cash so that the
duration gap is zero:
D gap  x cash  0.00  1  x cash average loan asset duration   Total Liabilitie s
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 D liabilities   0
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 Total assets
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Exploiting Comparative
Advantage in the Credit Market
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Interest rate swaps can be used to exploit
differentials in the credit market
Exploiting Comparative
Advantage in the Credit Market
Credit Market Example
AAA Bank and BBB Bank currently face the following
borrowing possibilities:
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Firm
Fixed Rate
Floating Rate
AAA
Current 5-yr
T-bond + 25 bp
LIBOR
BBB
Current 5-yr
T-bond + 85 bp
LIBOR + 30 bp
Quality Spread
60 bp
30 bp
Exploiting Comparative
Advantage in the Credit Market
Credit Market Example (cont’d)
AAA Bank has an absolute advantage over BBB in both the
fixed and the floating rate markets. AAA has a comparative
advantage in the fixed rate market.
The total gain available to be shared among the swap
participants is the differential in the fixed rate market minus
the differential in the variable rate market, or 30 bps.
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Exploiting Comparative
Advantage in the Credit Market
Credit Market Example (cont’d)
AAA Bank wants to issue a floating rate bond, while BBB
wants to borrow at a fixed rate. Both banks will borrow at a
lower cost if they agree to an interest rate swap.
AAA Bank should issue a fixed rate bond because it has a
comparative advantage in this market. BBB should borrow at
a floating rate. The swap terms split the rate savings 50-50.
The current 5-yr T-bond rate is 4.50%.
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Exploiting Comparative
Advantage in the Credit Market
Credit Market Example (cont’d)
LIBOR
AAA
Treasury + 40 bp
Treasury + 25 bp
Bondholders
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BBB
LIBOR +30 bp
Bondholders
Exploiting Comparative
Advantage in the Credit Market
Credit Market Example (cont’d)
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The net borrowing rate for AAA is LIBOR – 15 bps
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The net borrowing rate for BBB is Treasury + 70 bps
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The net rate for both parties is 15 bps less than without
the swap.
Foreign Currency Swaps
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In a currency swap, two parties
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Exchange currencies at the prevailing exchange
rate
Then make periodic interest payments to each
other based on a predetermined pair of interest
rates, and
Re-exchange the original currencies at the
conclusion of the swap
Foreign Currency Swaps
(cont’d)
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Cash flows at origination:
FX Principal
Party 1
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US $ Principal
Party 2
Foreign Currency Swaps
(cont’d)
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Cash flows at each settlement:
$ LIBOR
Party 1
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FX Fixed Rate
Party 2
Foreign Currency Swaps
(cont’d)
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Cash flows at maturity:
US $ Principal
Party 1
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FX Principal
Party 2
Foreign Currency Swaps
(cont’d)
Foreign Currency Swap Example
A multinational US corporation has a subsidiary in Germany.
It just signed a 3-year contract with a German firm. The
German firm will provide raw materials, with the US firm
paying 1 million Euros every 6 months for the 3-year period.
The current exchange rate is $0.90/Euro.
The contract is fixed in Euro terms, but if the dollar
depreciates against the Euro, dollar accounts payable would
increase.
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Foreign Currency Swaps
(cont’d)
Foreign Currency Swap Example (cont’d)
A currency swap is possible with the following terms:
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Tenor = 3 years
Notional value = 25 million Euros ($22.5 million)
Floating rate = $ LIBOR
Fixed rate = 8.00% on Euros
Foreign Currency Swaps
(cont’d)
Foreign Currency Swap Example (cont’d)
The swap will result in the following payments every six
months:
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Fixed rate payment = 25,000,000 Euros x 8.00% x 0.5 =
1,000,000 Euros
Floating rate payment = $22.5 million x 0.5 x LIBOR
Foreign Currency Swaps
(cont’d)
Foreign Currency Swap Example (cont’d)
Cash Flows at Origination
25 million euros
Party 1
Party 2
$22.5 million
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Foreign Currency Swaps
(cont’d)
Foreign Currency Swap Example (cont’d)
Cash Flows at Each Settlement
$ LIBOR
Party 1
Party 2
1 million euros
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Foreign Currency Swaps
(cont’d)
Foreign Currency Swap Example (cont’d)
Cash Flows at Maturity
$22.5 million
Party 1
Party 2
25 million euros
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Circus Swap
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Introduction
Swap variations
Introduction
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A circus swap combines an interest rate
and a currency swap
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Involves a plain vanilla interest rate swap and an
ordinary currency swap
Both swaps might be with the same
counterparty or with different counterparties
Introduction (cont’d)
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Circus swap with two counterparties:
8% on Euros
Party 1
Party 2
$ LIBOR
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Introduction (cont’d)
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Circus swap with two counterparties
(cont’d):
$ LIBOR
Party 1
Party 3
6.50% US
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Introduction (cont’d)
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Circus swap with two counterparties
(cont’d):
8% on Euros
Party 1
Net
6.50% US
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Introduction (cont’d)
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Circus swap with two counterparties
(cont’d):
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Party 1 is effectively paying 8% on Euros and
receiving 6.5% in U.S. dollars
Swap Variations
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Deferred swap
Floating for floating swap
Amortizing swap
Accreting swap
Deferred Swap
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In a deferred swap (forward start swap), the
cash flows do not begin until sometime
after the initiation of the swap agreement
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If the swap begins now, the deferred swap is
called a spot start swap
Floating for Floating Swap
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In a floating for floating swap, both parties
pay a floating rate, but with different
benchmark indices
Amortizing Swap
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In an amortizing swap, the notional value
declines over time according to some
schedule
Accreting Swap
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In an accreting swap, the notional value
increases through time according to some
schedule
Interest Rate Options
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Introduction
Interest rate cap
Interest rate floor
Calculating cap and floor payoffs
Interest rate collar
Swaption
Introduction
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Most of the trading done off the exchange
floors
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The interest rate options market is
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Very large
Highly efficient
Highly liquid
Easy to use
Introduction (cont’d)
Growth in Interest Rate Options
Notional Value
(Trillions)
15
10
5
0
1992 1993 1994 1995 1996 1997 1998 1999 2000
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Interest Rate Cap
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An interest rate cap
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Is like a portfolio of European call options
(caplets) on an interest rate
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On each interest payment date over the life of the cap,
one option in the portfolio expires
Is useful to firms with floating rate liabilities
Caps the periodic interest payments at the
caplet’s exercise price
Interest Rate Cap (cont’d)
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Long interest rate cap (exercise price 7%)
$ Payoff
Payoff
Option expires worthless
7%
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Floating Rate
Interest Rate Cap (cont’d)
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Short interest rate cap (exercise price 7%)
$ Payoff
Option expires worthless
7%
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Payout
Floating Rate
Interest Rate Floor
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An interest rate floor
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Is related to a cap in the same way that a put is
related to a call
Like a portfolio of European put options
(floorlets) on an interest rate
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On each interest payment date over the life of the cap,
one option in the portfolio expires
Is useful to firms with floating rate assets
Puts a lower limit on the periodic interest
payments at the floorlet’s exercise price
Interest Rate Floor (cont’d)
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Long interest rate floor (exercise price 6.5%)
$ Payoff
Payoff
Option expires worthless
6.5%
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Floating Rate
Interest Rate Floor (cont’d)
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Short interest rate floor (exercise price 6.5%)
$ Payoff
Option expires worthless
Payout
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6.5%
Floating Rate
Calculating Cap and Floor
Payoffs
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There are no universally acceptable terms
to caps and floors
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However, frequently the terms provide for
the cash payment on an in-the-money
caplet or floorlet to be based on a 360-day
year
Calculating Cap and Floor
Payoffs (cont’d)
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Cap payout formula:
Days in payment period
Cap payout  (notional value) 

360
(benchmark rate - striking price)
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If the benchmark rate is less than the
exercise price, the payout is zero
Calculating Cap and Floor
Payoffs (cont’d)
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Floor payout formula:
Days in payment period
Floor payout  (notional value) 

360
(striking price - benchmark rate)
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Interest Rate Collar
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An interest rate collar is simultaneously
long an interest rate cap and short an
interest rate floor
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Sacrifices some upside potential in
exchange for a lower position cost
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Premium from writing the floorlets reduces
position costs
Interest Rate Collar (cont’d)
Long cap
$ Payoff
Inflow
No payout
Outflow
K1
Short floor
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K2
Floating Rate
Swaption
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A swaption is an option on a swap
Can be either American or European style
A payer swaption (put swaption) gives its
owner the right to pay the fixed interest rate
on a swap
A receiver swaption (call swaption) gives its
owner the right to receive the fixed rate and
pay the floating rate