Swap Derivatives:
Forward Swaps and Swaptions
1
Swap Derivatives
 Today, there are a number of nonstandard or non-generic
swaps used by financial and non-financial corporations to
manage their varied cash flow and asset and liability
positions.
 Two of the most widely used non-generic swaps are the
forward swap and options on swaps or swaptions.
 A forward swap is an agreement to enter into a swap that
starts at a future date at an interest rate agreed upon today.
 A swaption, in turn, is a right, but not an obligation, to take
a position on a swap at a specific swap rate.
2
Forward Swaps
 Like futures and farward contracts on debt
securities, forward swaps provide borrowers and
investors with a tool for locking in a future
interest rate.
 As such, they can be used to manage interest rate
risk for fixed-income positions.
3
Hedging a Future Loan
with a Forward Swap
Financial and non-financial institutions that
have future borrowing obligations can lock
in a future rate by obtaining forward
contracts on fixed-payer swap positions.
4
Hedging a Future Loan


Example:
A company wishing to lock in a rate on a 5-year, fixedrate $100,000,000 loan to start two years from today,
could enter a 2-year forward swap agreement to pay
the fixed rate on a five-year 9%/LIBOR swap.
At the expiration date on the forward swap, the
company could issue $100,000,000 floating-rate debt
at LIBOR that, when combined with the fixed position
on the swap, would provide the company with a
synthetic fixed rate loan paying 9% on the floating
debt.
5
Hedging a Future Loan
Instrument
Action
Issue Flexible Rate Note
Swap: Fixed-Rate Payer’s Position
Swap: Fixed-Rate Payer’s Position
Pay LIBOR
Pay Fixed Rate
−LIBOR
Receive LIBOR
+LIBOR
Synthetic Fixed Rate
Net Payment
−9%
9%
6
Hedging a Future Loan

Alternatively, at the forward swap’s expiration date,
the company could sell the 5-year 9%/LIBOR swap
underlying the forward swap contract and issue a 5year fixed-rate bond.

If the rate on 5-year fixed rate bond were higher than
9%, for example at 10%, then the company would be
able offset the higher interest by selling its fixed
position on the 9%/LIBOR swap to a swap dealer for
an amount equal to the present value of a 5-year
annuity equal to 1% (difference in rates: 10% − 9%)
times the NP.
7
Hedging a Future Loan
 For example, at 10% the value of the underlying
9%/LIBOR swap would be $3.8609 million
using the YTM swap valuation approach:
SV
fix
 10 (.10 / 2)  (.09 / 2) 
 
$100 million  $3.8609 million

t
 t 1 (1  (.10 / 2)) 
8
Hedging a Future Loan

With the proceeds of $3.8609 million from closing its
swap, the company would only need to raise $96.1391
million (= $100 million − $3.8609 million).

The company, though, would have to issue $96.1391
million worth of 5-year fixed-rate bonds at the higher
10% rate.

This would result in semiannual interest payments of
$4.8070 million (= (.10/2)($96.1391 million), and the
total return based on the $100 million funds needed
would be approximately 9%.
9
Hedging a Future Loan

If the rate on 5-year fixed rate loans were lower than 9%, say 8%,
then the company would benefit from the lower fixed rate loan, but
would lose an amount equal to the present value of a 5-year annuity
equal to 1% (difference in rates: 8% − 9%) times the NP when it
closed the fixed position.

Specifically, at 8%, the value of the underlying 9%/LIBOR swap is
−$4.055 million using the YTM approach:
 10 (.08 / 2)  (.09 / 2) 
SV  
$100 million

t
 t 1 (1  (.08 / 2)) 
SV fix   $4.055 million
fix
10
Hedging a Future Loan

The company would therefore have to pay the swap bank $4.055
million for assuming its fixed-payer’s position.

With a payment of $4.055 million, the company would need to raise a
total of $104.055 million from its bond issue.

The company, though, would be able to issue $104.055 million worth
of 5-year fixed-rate bonds at the lower rate of 8% rate.

Its semiannual interest payments would be $4.1622 million (=
.08/2)($104.055 million), and its total return based on the $100
million funds needed would be approximately 9%.
11
Hedging a Future Investment

Forward swaps can also be used on the asset side to fix
the rate on a future investment.

Consider the case of an institutional investor planning to
invest an expected $10 million cash inflow one year from
now in a 3-year, high quality fixed-rate bond.

The investor could lock in the future rate by entering a 1year forward swap agreement to receive the fixed rate and
pay the floating rate on a 3-year, 9%/LIBOR swap with a
NP of $10 million.
12
Hedging a Future Investment

At the expiration date on the forward swap, the
investor could invest the $10 million cash inflow in
a 3-year FRN at LIBOR that, which when combined
with the floating position on the swap, would
provide the investor with a synthetic fixed rate-loan
paying 9%.
13
Hedging a Future Investment
Instrument
Buy Flexible Rate Note
Swap: Floating-Rate Payer’s Position
Swap: Floating-Rate Payer’s Position
Synthetic Fixed Rate Investment
Action
Receive LIBOR
Pay LIBOR
LIBOR
−LIBOR
Receive Fixed Rate
+9%
Net Receipt
9%
14
Hedging a Future Investment

Instead of forming a synthetic fixed investment
position, the investor alternatively could sell the 3-year
9%/LIBOR swap underlying the forward swap
contract and invest in a 3-year fixed-rate note.

If the rate on the 3-year fixed rate note were lower than
the 9% swap rate, then the investor would be able to
sell his floating position at a value equal to the present
value of an annuity equal to the $10 million NP times
the difference between 9% and the rate on 3-year fixed
rate bonds; this gain would offset the lower return on
the fixed-rate bond.
15
Hedging a Future Investment

Example:
If at the forward swaps’ expiration date, the rate on 3-year,
fixed rate bonds were at 8%, and the fixed rate on a 3-year
par value swap were at 8%, then the investment firm
would be able to sell its floating-payer’s position on the 3year 9%/LIBOR swap underlying the forward swap
contract to a swap bank for $262,107 (using the YTM
approach with a discount rate of 8%):
6

(.09 / 2)  (.08 / 2) 
fl
SV  
$10,000,000  $262,107
t 
 t 1 (1  (.08 / 2)) 
16
Hedging a Future Investment

The investment firm would therefore invest $10
million plus the $262,107 proceeds from closing its
swap position.

The total return based on an investment of $10
million, though, would be approximately equal to
9%.
17
Hedging a Future Investment

On the other hand, if the rate on 3-year fixed-rate
securities were higher than 9%, the investment company
would benefit from the higher investment rate, but
would lose on closing its swap position.

Example: If at the forward swap’s expiration date, the
rate on 3-year, fixed rate bonds were at 10% and the
fixed rate on a 3-year par value swap were at 10%, then
the investment firm would have to pay the swap bank
$253,785 for assuming its floating-payer’s position on
the 3-year 9%/LIBOR swap underlying the forward
swap contract:
 6 (.09 / 2)  (.10 / 2) 
SV  
$10,000,000   $253,785
t 
 t 1 (1  (.10 / 2)) 
fl
18
Hedging a Future Investment

The investment firm would therefore invest
$9,746,215 ($10,000,000 minus the $253,785 costs
incurred in closing its swap) in 3-year, fixed rate
bonds yielding 10%.

The total return based on an investment of $10
million funds, though, would be approximately
equal to 9%.
19
Other Uses of Forward Swaps

The examples illustrate that forward swaps are like
futures on debt securities.

As such, they are used in many of the same ways as
futures:
1.
2.
3.

Locking in future interest rates
Speculating on future interest rate changes
Altering a balance sheet’s exposure to interest rate changes
Different from futures, though, forward swaps can be
customized to fit a particular investment or borrowing
need and with the starting dates on forward swaps
ranging anywhere from one month to several years, they
can be applied to not only short-run but also long-run
positions.
20
Swaptions

One of the most innovative non-generic swaps is the
swap option or simply swaption.

As the name suggests, a swaption is an option on a swap.

The purchaser of a swaption buys the right to start an
interest rate swap with a specific fixed rate or exercise
rate, and with a maturity at or during a specific time
period in the future.

If the holder exercises, she takes the swap position, with
the swap seller obligated to take the opposite
counterparty position.

For swaptions, the underlying instrument is a forward
swap and the option premium is the up-front fee.
21
Swaptions

The swaption can be either a receiver swaption or a
payer swaption:

A receiver swaption gives the holder the right to
receive a specific fixed rate and pay the floating rate


The right to take a floating payer’s position
A payer swaption gives the holder the right to pay a
specific fixed rate and receive the floating rate

The right to take a fixed payer’s position
22
Swaptions
Swaptions can be either European or
American:
 A European swaption can be exercised only at a
specific point in time, usually just before the
starting date on the swap.
 An American swaption is exercisable at any point
in time during a specified period of time.
23
Swaptions

Swaptions are similar to interest rate options or
options on debt securities. They are, however, more
varied:
1.
They can range from options to begin a 1-year
swap in 3 months to a 10-year option on a 8-year
swap (sometimes referred to as a 10 x 8 swaption).
2.
The exercise periods can vary for American
swaptions.
3.
Swaptions can be written on generic swaps or nongeneric swaps.
24
Swaptions
 Like interest rate and debt options, swaptions
can be used for:
1. Speculating on interest rates
2. Hedging debt and asset positions against market
risk
3. Combined with other securities to create
synthetic positions
25
Swaptions: Speculation
 Suppose a speculator expects the rate on high
quality, 5-year fixed rate bonds to increase from
their current 8% level.
 As an alternative to a short T-note futures
position or an interest rate call, the speculator
could buy a payer swaption.
26
Swaptions: Speculation

Suppose the speculator elects to buy a 1-year European
payer swaption on a 5-year, 8%/LIBOR swap with a
NP of $10,000,00 for 50 bp times the NP:
1. 1 x 5 payer swaption
2. Exercise date = 1 year
3. Exercise rate = 8%
4. Underlying swap = 5-year, 8%/LIBOR with NP
= $10,000,000
5. Swap position = fixed payer
6. Option premium = 50 bp times NP
27
Swaptions: Speculation

On the exercise date, if the fixed rate on a 5-year
swap were greater than the exercise rate of 8%, then
the speculator would exercise her right to pay the
fixed rate below the market rate.

To realize the gain, she could take her 8% fixed-rate
payer’s swap position obtained from exercising and
sell it to another counterparty.
28
Swaptions: Speculation

For example, if the 5-year par value swap were trading at
9% and swaps were valued by the YTM approach, then
she would be able to sell her 8% swap for $395,636:
 10 (.09 / 2)  (.08 / 2) 
Value of Swap  
($10,000,000)

t
 t 1 (1  (.09 / 2)) 
Value of Swap  $395,636

If the swap rate at the expiration date were less than 8%,
then the payer swaption would have no value and the
speculator would simple let it expire, losing the premium
she paid.
29
Swaptions: Speculation

Formally, the value of the payer swaption at expiration is:
 10 Max[(R / 2)  (.08 / 2), 0] 
Value of Swap  
($10,000,000)

t
(1  (R / 2))
 t 1



For rates, R, on par value 5-year swaps exceeding the exercise rate of
8%, the value of the payer swaption will be equal to the present value
of the interest differential times the notional principal on the swap.

For rates less than or equal to 8%, the swap is worthless.
The next slide shows graphically and in a table the values and
profits at expiration obtained from closing the payer swaption
on the 5-year 8%/LIBOR swap given different rates at
expiration.
30
Value and Profit at Expiration
from 8%/LIBOR Payer Swaption
Rates on 5-year Par Value
Swaps at Expiration
R
0.060
0.065
0.070
0.075
0.080
0.085
0.090
0.095
0.100
Payer Swaption's
Interest Differential
Max((R−.08)/2,0)
0.0000
0.0000
0.0000
0.0000
0.0000
0.0025
0.0050
0.0075
0.0100
Value of 8%/LIBOR
Payer Swaption at Expiation
PV(Max[(R−.08)/2, 0]($10m))
$0
$0
$0
$0
$0
$200,272
$395,636
$586,226
$772,173
Payer Swaption
Cost
Profit from Payer
Swaption
$50,000
$50,000
$50,000
$50,000
$50,000
$50,000
$50,000
$50,000
$50,000
-$50,000
-$50,000
-$50,000
-$50,000
-$50,000
$150,272
$345,636
$536,226
$722,173
31
Swaptions: Speculation

Instead of higher rates, suppose the speculator expects
rates on 5-year high quality bonds to be lower one year
from now.

In this case, her strategy would be to buy a receiver
swaption.
32
Swaptions: Speculation

If she bought a receiver swaption similar in terms to
the above payer swaption (1-year receiver option on
a 5-year, 8%/LIBOR swap), and the swap rate on a
5-year swap were less than 8% on the exercise date,
then she would realize a gain from exercising and
then either selling the floating-payer’s position or
combining it with a fixed-payer’s position on a
replacement swap.
33
Swaptions: Speculation

For example, if the fixed rate on a 5-year par value swap
were 7%, the investor would exercise her receiver
swaption by taking the 8% floating-rate payer’s swap and
then sell the position to another counterparty.

With the current swap rate at 7% she would be able to sell
the 8% fixed-payer’s position for $415,830:
 10 (.08 / 2)  (.07 / 2) 
Value of Swap  
($10,000,000)  $415,830

t
 t 1 (1  (.07 / 2)) 

If the swap rate were higher than 8% on the exercise date,
then the investor would allow the receiver swaption to
expire, losing, in turn, her premium.
34
Swaptions: Speculation

Formally, the value of the 8%/LIBOR receiver swaption at expiration
is
 10 Max[(.08 / 2)  (R / 2), 0] 
Value of Swap  
($10,000,000)

t
(1  (R / 2))
 t 1


For rates, R, on par value 5-year swaps less than the exercise rate of
8%, the value of the receiver swaption will be equal to the present
value of the interest differential times the notional principal on the
swap.

For rates equal to or greater than 8%, the swap is worthless.

The next slide shows graphically and in a table the values and profits at
expiration obtained from closing the receiver swaption on the 5-year
8%/LIBOR swap given different rates at expiration.
35
Value and Profit at Expiration
from 8%/LBOR Receiver Swaption
Rates on 5-year Par Value
Swaps at Expiration
R
0.060
0.065
0.070
0.075
0.080
0.085
0.090
0.095
0.100
Receiver Swaption's
Value of 8%/LIBOR
Receiver Swaption
Profit from
Interest Differential Receiver Swaption at Expiation
Cost
Receiver Swaption
PV(Max[(.08−R)/2, 0]($10m))
Max((.08-R)/2,0)
0.0100
$853,020
$50,000
$803,020
0.0075
$631,680
$50,000
$581,680
0.0050
$415,830
$50,000
$365,830
0.0025
$205,320
$50,000
$155,320
0.0000
$0
$50,000
-$50,000
0.0000
$0
$50,000
-$50,000
0.0000
$0
$50,000
-$50,000
0.0000
$0
$50,000
-$50,000
0.0000
$0
$50,000
-$50,000
36
Swaptions: Hedging
 Like other option hedging tools, swaptions
give investors or borrowers protection
against adverse interest rate movements, but
still allow them to benefit if rates move in
their favor.
37
Swaptions: Hedging
 As a hedging tool, swaptions serve as a rateprotection tool:
 As rates increase, the value of the payer swaptions
increases in value, making the payer swaption act as
a cap on the rates paid on debt positions.
 As rates decrease, receiver swaptions increase in
value, making them act as a floor on the rates earned
from asset positions.
38
Swaptions: Floor

To illustrate how receiver swaptions are used for
establishing a floor, consider the case of a fixedincome investment fund that has a Treasury bond
portfolio worth $30,000,000 in par value that is
scheduled to mature in 2 years.

Suppose the fund plans to reinvest the $30,000,000
in principal for another 3 years in Treasury notes that
are currently trading to yield 6%, but is worried that
interest rate could be lower in two years.
39
Swaptions: Floor

To establish a floor on its investment, suppose the
fund purchased a 2-year receiver swaption on a 3year, 6%/LIBOR generic swap with a notional
principal of $30,000,000 from First Bank for
$100,000.
40
Swaptions: Floor

The next slide shows:
1. The values that the fund would obtain from closing its
receiver swaption given different rates at the swaption’s
expiration.
2. The hedged total return it would obtain from reinvesting for
3 years the $30,000,000 plus the proceeds from the swaption
based on $30,000,000 investment and the assumption of a
flat yield curve.
41
Swaptions: Floor
Rates on 3-year Par Value
Receiver Swaption's
Swaps and T-notes at Expiration Interest Differential
R
Max((.06-R)/2,0)
0.040
0.0100
0.045
0.0075
0.050
0.0050
0.055
0.0025
0.060
0.0000
0.065
0.0000
0.070
0.0000
0.075
0.0000
0.080
0.0000
Value of 6%/LIBOR
Receiver Swaption at Expiation
PV(Max[(.06-R)/2, 0]($30m))
$1,680,429
$1,249,757
$826,219
$409,678
$0
$0
$0
$0
$0
Receiver Swaption Profit from
Funds Invested
Cost
Swaption $30m + Swaption Value
$100,000
$100,000
$100,000
$100,000
$100,000
$100,000
$100,000
$100,000
$100,000
$1,580,429
$1,149,757
$726,219
$309,678
-$100,000
-$100,000
-$100,000
-$100,000
-$100,000
$31,680,429
$31,249,757
$30,826,219
$30,409,678
$30,000,000
$30,000,000
$30,000,000
$30,000,000
$30,000,000
Rate
0.059
0.059
0.059
0.060
0.060
0.065
0.070
0.075
0.080
  ($30,000,000  Swap Value)(1  (R / 2))6 1/ 6


Rate  T R  2 
 1



$30,000,000



42
Swaptions: Floor

As shown in the exhibit slide, for rates less than 6%
the swaption values increase as rates fall, in turn,
offsetting the lower investment rates and yielding a
rate on the investment of approximately 6%.

On the other hand, for rates equal or greater than 6%,
the swaption are worthless, whereas the investment’s
total return increases as rates increase.

Thus, for the cost of $100,000, the receiver swaption
provides the fund a floor with a rate of 6%.
43
Swaptions: Cap

In contrast to the use of swaptions to establish a floor
on an investment, suppose a firm had a future debt
obligation whose rate it wanted to cap. In this case,
the firm could purchase a payer swaption.

To illustrate, suppose a company has a $60,000,000,
9% fixed-rate bond obligation maturing in 3 years that
it plans to finance by issuing new 5-year fixed-rate
bonds.

Suppose the company is worried that interest rates
could increase in 3 years and as a result wants to
establish a cap on the rate it would pay on its future 5year bond issue.
44
Swaptions: Cap

To cap the rate, suppose the company purchases a 3year payer swaption on a 5-year, 9%/LIBOR generic
swap with notional principal of $60,000,000 from First
Bank for $200,000.

The next slide shows for different rates at expiration,
the values the company would obtain from closing its
payer swaption and the hedged rate (based on
$60,000,000 debt and the assumption of a flat yield
curve) it would obtain from borrowing for five years
the $60,000,000 minus the proceeds from the
swaption.
45
Swaptions: Cap
Rates on 5-year Par Value
Payer Swaption's
Value of 9%/LIBOR
Swaps and Bond at Expiration Interest Differential Payer Swaption at Expiation
R
Max((R-.09)/2,0)
PV(Max[(R-.09)/2, 0]($60m))
0.070
0.0000
0
0.075
0.0000
0
0.080
0.0000
0
0.085
0.0000
0
0.090
0.0000
0
0.095
0.0025
1,172,452
0.100
0.0050
2,316,520
0.105
0.0075
3,432,978
0.110
0.0100
4,522,575
Payer Swaption
Cost
Profit from Payer
Funds Borrowed
Swaption
$60m − Swaption Value
200,000
200,000
200,000
200,000
200,000
200,000
200,000
200,000
200,000
-200,000
-200,000
-200,000
-200,000
-200,000
972,452
2,116,520
3,232,978
4,322,575
60,000,000
60,000,000
60,000,000
60,000,000
60,000,000
58,827,548
57,683,480
56,567,022
55,477,425
Rate
0.070
0.075
0.080
0.085
0.090
0.091
0.092
0.093
0.094
  ($60,000,000  Swap Value)(1  (R / 2))10 1/10


Rate  T R  2 
 1



$60,000,000



46
Swaptions: Cap

As shown in the exhibit slide, for rates greater than
9% the swaption values increase as rates increase, in
turn, offsetting the higher borrowing rates and
yielding a total return on the hedged bond issue of
approximately 9%.

On the other hand, for rates less than 9%, the
swaption are worthless whereas the debt’s rate
decreases as rates decrease.

Thus, for the cost of $200,000, the payer swaption
provides the fund a cap on it future debt with a cap
rate of 9%.
47
Hedging the Risk of
Embedded Call Option

Swaptions can also be used to hedge against the
impacts that adverse interest rate changes have on
investment and debt positions with embedded options.

Consider a fixed-income manager holding
$10,000,000 worth of 10-year, high quality, 8% fixedrate bonds that are callable in two years at a call price
equal to par.
48
Hedging the Risk of
Embedded Call Option

Suppose the manager expects a decrease in rates over
the next two years, increasing the likelihood that his
bonds will be called and he will be forced to reinvest
in a market with lower rates.

To minimize his exposure to this call risk, suppose the
manager buys a 2-year receiver swaption on an 8-year,
8%/LIBOR swap with a NP of $10,000,000.
49
Hedging the Risk of
Embedded Call Option

If two years later, rates were to increase, then the
bonds would not be called and the swaption would
have no value.

In this case, the fixed income manager would lose the
premium he paid for the receiver swaption.
50
Hedging the Risk of
Embedded Call Option

However, if two years later, rates on 8-year bonds were
lower at say 6%, and the bonds were called at a call
price equal to par, then the manager would be able to
offset the loss from reinvesting the call proceed at
lower interest rate by the profits from exercising the
receiver swaption.
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Hedging the Risk of
Embedded Put Option

The contrasting case of a fixed-income manager
hedging callable bonds would be the case of a financial
manager who issued putable bonds some time ago and
was now concerned that rates might increase in the
future.

If rates did increase and bondholders exercised their
option to sell the bonds back to the issuer at a specified
price, the issuer would have to finance the purchase by
issuing new bonds paying higher rates.

To hedge against this scenario, the financial manager
could buy a payer swaption with a strike rate equal to
the coupon rate on the putable bonds.
52
Hedging the Risk of
Embedded Put Option

If the current swap rate exceeded the strike rate and the
bonds were put back to the issuer, the manager could
exercise his payer swaption to take the fixed payer
position at the strike rate and then sell the swap and use
the proceeds to defray part of higher financing cost of
buying the bonds on the put.

On the other hand, if rates were to decrease, then the
put option on the bond would not be exercised and the
payer swaptions would have no value. In this case, the
manager would lose the swaption premium.
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Synthetic Positions

With swaptions, generic swaps, and non-generic
swaps, there are a number of synthetic asset and
liability permutations: Callable and putable debt,
callable and putable bonds, flexible rate securities, and
flexible-rate debt.

Example: A company that wants to finance a
$50,000,000 capital expenditure with 7-year, optionfree, 9% fixed-rate debt could issue 7-year, optionfree, fixed-rate bonds or create a synthetic 7-year bond
by issuing 7-year FRNs and taking a fixed-payer’s
position on a 7-year swap.
54
Synthetic Positions

With swaptions, as well as other non-generic swaps,
there are actually several other ways in which this
synthetic fixed-rate bond could be created.

For example, to obtain an option-free, fixed-rate bond,
the company could issue a callable bond and then sell a
receiver swaption with terms similar to the bond.

This synthetic debt position will provide a lower rate
than the rate on a direct loan if investors underprice the
call option on callable debt.
55
Cancelable and Extendable Swaps

Swaps can have clauses giving the counterparty the
right to extend the option or to cancel the option.

These swaps are known as cancelable and extendable
swaps.

Analogous to bonds with embedded call and put
options, these swaps are equivalent to swaps with
embedded payer swaptions and receiver swaption.
56
Cancelable Swap

A cancelable swap is a swap in which one of the
counterparties has the option to terminate one or more
payments.

Cancelable swaps can be callable or putable.
57
Cancelable Swap

A callable swap is one in which the fixed payer has
the right to early termination.


Thus, if rates decrease, the fixed-rate payer on the swap with
this embedded call option to early termination can exercise
her right to cancel the swap.
A putable swap is one in which the floating payer has
the right to early cancellation.

A floating-rate payer with this option may find it
advantageous to exercise his early-termination right when
rates increase.
58
Cancelable Swap

Note:
If there is only one termination date, then a cancelable
swap is equivalent to a standard swap plus a position in
a European swaption.
59
Cancelable Swap

A 5-year putable swap to receive 6% and pay LIBOR that is cancelable after
two years is equivalent to a floating position in a 5-year 6%/LIBOR generic
swap and a long position in a 2-year payer swaption on a 3-year 6%/LIBOR
swap.
5-year Putable Swap
• Pay LIBOR and receive 6%
fixed rate
• Cancelable after 2 years

≡
• A floating position in a 5-year, 6%/LIBOR
generic swap
and
• A long position in a 2-year payer swaption
on a 3-year, 6%/LIBOR swap.
After two years, the payer swaption gives the holder the right to take a fixedpayer’s position on a 3-year swap at 6% that offsets the floating position on
the 6% generic swap.
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Cancelable Swap

A 5-year callable swap to pay 6% and receive LIBOR that is cancelable after
two years would be equivalent to a fixed position in a 5-year 6%/LIBOR generic
swap and a long position in a 2-year receiver swaption on a 3-year 6%/LIBOR
swap.
5-year Callable Swap
• Pay 6% fixed Rate and
receive LIBOR
• Cancelable after 2 years

≡
• A fixed position in a 5-year, 6%/LIBOR
generic swap
and
• A long position in a 2-year receiver swaption
on a 3-year, 6%/LIBOR swap.
After two years, the receiver swaption gives the holder the right to take a
floating-payer’s position on a 3-year swap at 6% that offsets the fixed-payer’s
position on the 6% generic swap.
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Extendable Swap

An extendable swap is just the opposite of a
cancelable swap.

It is a swap that has an option to lengthen the terms of
the original swap.

The swap allows the holder to take advantage of
current rates and extend the maturity of the swap.
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Extendable Swap

Like cancelable swaps, extendable swaps can be
replicated with a generic swap and a swaption.

The floating payer with an extendable option has the
equivalent of a floating position on a generic swap
and a receiver swaption.

The fixed payer with an extendable option has the
equivalent of a fixed position on a generic swap and a
payer swaption.
63
Extendable Swap

Floating Payer Extendable Swap
A 3-year floating payer swap to pay LIBOR and receive a 6% fixed rate that
is extendable at maturity to two more years would be equivalent to a floating
position in a 3-year 6%/LIBOR generic swap and a long position in a 3-year
receiver swaption on a 2-year 6%/LIBOR.
3-Year Floating Payer Extendable Swap
•3-year floating-payer swap to pay
LIBOR and receive 6%
• Extendable after 2 years

≡
• A floating payer position on a 3-year
6%/LIBOR generic swap
and
• A long position in a 3-year receiver
swaption on a 2-year, 6%/LIBOR swap
At the end of 3 years, the receiver swaption gives the holder the right to take
a floating-payer’s position on a 2-year swap at 6% which in effect extends
the maturity of the expiring floating position on the 6% generic swap.
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Extendable Swap

Fixed Payer Extendable Swap
A 3-year fixed payer swap to pay 6% fixed rate and receive LIBOR that is
extendable at maturity to two more years would be equivalent to a fixed
position in a 3-year 6%/LIBOR generic swap and a long position in a 3-year
payer swaption on a 2-year 6%/LIBOR.
3-Year Fixed Payer Extendable Swap
•3-year fixed-payer swap to pay 6% and
receive LIBOR
• Extendable after 2 years

≡
• A fixed payer position on a 3-year
6%/LIBOR generic swap
and
• A long position in a 3-year payer
swaption on a 2-year, 6%/LIBOR swap.
At the end of 3 years, the payer swaption gives the holder the right to take a
fixed-rate payer’s position on a 2-year swap at 6% which in effect extends
the maturity of the expiring fixed-payer’s position on the 6% generic swap.
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Cancelable and Extendable Swaps:
Synthetic Positions

Because cancelable and extendable swaps are equivalent
to generic swaps with a swaption, they can be used like
swaptions to create synthetic positions.

For example, the synthetic fixed-rate debt position
formed by issuing FRNs and taking a fixed-payer’s
position on a generic swap could also be created by:
1. Issuing callable bonds
2. Taking a fixed payer’s position on a generic swap
3. Taking a floating payer’s position on a callable
swap
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Cancelable and Extendable Swaps:
Synthetic Positions
 The synthetic fixed-rate debt position also
could be formed by:
1. Issuing putable bonds
2. Taking a fixed-payer’s position on a generic
swap
3. Taking a floating position on a putable swap
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Non-Generic Swaps

Today, there are a number of non-generic swaps used
by financial and non-financial corporations to manage
their varied cash flow and return-risk problems.

non-generic swaps usually differ in terms of their rates,
principal, or effective dates.

For example, instead of defining swaps in terms of the
LIBOR, some swaps use the T-bill rate or the prime
lending rate.
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Non-Generic Swap

In a total return swap, the return from one asset or
portfolio of assets is swapped for the return on another
asset or portfolio.

These swaps can be used to pass credit risk onto another
party or to achieve a more diversified portfolio.

For example, a California bank with a relatively heavy
proportion of loans to technology companies could enter
into a swap with a Michigan bank with a relatively large
proportion of loans to auto-related companies.
69
Non-Generic Swap

In an equity swap, one party agrees to pay the return
on an equity index, such as the S&P 500, and the
other party agrees to pay a floating rate (LIBOR) or
fixed rate.

For example, on an S&P 500/LIBOR swap, the
equity-payer would agree to pay the 6-month rate of
change on the S&P 500 (e.g., proportional change in
the index between effective dates) times a NP in
return for LIBOR times NP, and the debt payer would
agree to pay the LIBOR in return for the S&P 500
return.

Equity swaps are useful to fund managers who want
to increase or decrease the equity exposure of their
portfolios.
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Non-Generic Swap

An amortizing swap is one in which the NP decreases
over time based on a set schedule. Amortizing swaps
can be used by companies that have fixed-rate
borrowing obligations with a certain prepayment
schedule, but would like to swap them for floating
rates.

An accreting swap (also called set-up swap) is one in
which the NP increases over time based on a set
schedule. An accreting swap is useful to companies that
plan to borrow increasing amounts at floating rates and
want to swap them for fixed-rate funds; accreting
swaps are particularly popular in construction
financing.
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Non-Generic Swap

Basis Swap: Both rates are floating; each party
exchanges different floating payments: One party
might exchange payments based on LIBOR and the
other based on the T-bill yield.

Delayed-Rate Set Swap allows the fixed payer to wait
before locking in a fixed swap rate – the opposite of a
forward swap.

Delayed-Reset Swap: The effective date and payment
date are the same. The cash flows at time t are
determined by the floating rate at time t rather than
the rate at time t −1.
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Non-Generic Swaps: Summary
1.
Non-LIBOR Swap: Swaps with floating rates different than LIBOR. Example: Tbill rate, CP rate, or Prime Lending Rate.
2.
Delayed-Rate Set Swap allows the fixed payer to wait before locking in a fixed
swap rate – the opposite of a forward swap.
3.
Zero-Coupon Swap: Swap in which one or both parties do not exchange
payments until maturity on the swap.
4.
Prepaid Swap: Swap in which the future payments due are discounted to the
present and paid at the start.
5.
Delayed-Reset Swap: The effective date and payment date are the same. The
cash flows at time t are determined by the floating rate at time t rather than the
rate at time t − 1.
6.
Amortizing Swaps: Swaps in which the NP decreases over time based on a set
schedule.
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Non-Generic Swaps: Summary
7.
Set-Up Swap or Accreting Swap: Swaps in which the NP increases over time
based on a set schedule
8.
Index Amortizing Swap: Swap in which the NP is dependent on interest rates.
9.
Equity Swap: Swap in which one party pays the return on a stock index and the
other pays a fixed or floating rate.
10. Basis Swap: Swaps in which both rates are floating; each party exchanges
different floating payments: One party might exchange payments based on
LIBOR and the other based on the T-bill yield.
11. Total Return Swap: Returns from one asset are swapped for the returns on
another asset.
12. Non-U.S. Dollar Interest Rate Swap: interest-rate swap in a currency different
than U.S. dollar with a floating rate often different than the LIBOR: Frankfort
rate (FIBOR), Vienna (VIBOR), and the like.
74