swap variations

Question 1

A swap is

Answer 1

an agreement between two parties
to exchange cashflows in the future.

The agreement defines
the dates when the cashflows are to be paid and
the way that they are to be calculated.

Usually, the calculation of the cashflows involves 
the future values of 
one or more market variables 
(eg 
interest rates, 
security prices, 
commodity prices or 
currencies).

Question 2

In a “plain vanilla” interest rate swap (also known as a “par swap”)

Answer 2

Company B agrees to pay Company A 
cashflows 
equal to interest at a 
predetermined fixed rate 
on a notional principal 
for a number of years. 

At the same time, 
Company A agrees to pay Company B 
cashflows equal to interest at a 
floating rate 
on the same notional principal 
for the same period of time. 

The currencies of the two sets of cashflows
are the same.

Question 3

For swaps note that

Answer 3

1 The notional principal
⁃ is used only for the calculation of interest payments.
⁃ The principal itself is not exchanged. 


2 The floating-rate payment to be paid at a particular date is
⁃ usually based on the value of the relevant floating rate
⁃ at the previous cashflow payment date.
⁃ This means that at
⁃ any time
⁃ the monetary amount of the next floating payment
⁃ is always known.
⁃ In many interest rate swaps, the floating rate is LIBOR. 


3  The phrase plain vanilla is used here because we are referring to the most basic form of interest rate swap.
⁃ Other more complicated swaps are often referred to as
⁃ exotic swaps. 


Question 4

What is LIBOR?

Answer 4

LIBOR is short for the London Interbank Offered Rate.
a LIBOR rate is the short-term spot interest rate
at which one large international bank
is willing to lend money to another large international bank.
specifically, LIBOR rates are
the rates of interest offered between
Eurocurrency banks
for fixed-term deposits.

Question 5

A series of LIBOR rates exists for different terms

Answer 5

(from overnight lending up to 12 months) 
in many of the major currencies. 
These include the
 Euro, 
US dollars, 
UK sterling, 
Japanese yen, 
Swiss francs, 
Australian dollars and 
New Zealand dollars.

Question 6

LIBOR zero rates are generally

Answer 6

higher than the corresponding Treasury Bill rates.
This is because they are not risk-free,
as banks are able to default on their loans.

Question 7

The floating-rate payments under many interest rate derivatives are based on

Answer 7

LIBOR rates.

Question 8

cashflows under a “plain vanilla” swap.

Answer 8

Example
5-year interest rate swap
based on a notional principal of $50 million.
Under the terms of the swap,
Company B agrees to make interest payments annually in arrears
based on a fixed interest rate of 6% pa,
in return for which Company A makes
corresponding variable interest rate payments
based on the 1-year (spot) LIBOR rate.
The cashflows paid can be represented in a diagram.

Question 9

Using a swap to transform the nature of the liabilities

Answer 9

The swap contract has the effect of 
transforming the nature of the liabilities. 
In the example above, Company B 
can use the swap 
to transform a 
floating-rate loan into a fixed-rate loan, 
while, for Company A, 
the swap has the effect of
 transforming a fixed-rate loan into 
a floating-rate loan.

Question 10

swaps can be used to transform the nature of an asset

Answer 10

from one earning
a fixed rate of interest into one
earning a floating rate of interest
(or vice versa).

Question 11

Arranging a swap

Answer 11

Usually, two non-financial companies
do not get in touch directly to arrange a swap.
They each deal with a financial intermediary
(such as a bank)
which is remunerated
by the difference
between the value of
a pair of offsetting transactions,
providing neither client defaults on their swap.

Question 12

Interest rate swap with a bank as intermediary example

Answer 12

 A is a net borrower at a floating rate of LIBOR + 0.35% pa, ie 0.1% pa more than before 


 B is a net borrower at a fixed rate of 6.6% pa, ie 0.1% pa more than before 


 providing neither A nor B defaults on their swap, the bank as intermediary will end up making a profit of 0.2% pa on the principal of $50 million, ie $100,000 pa for the 5-year life of the swap.

Question 13

In practice, any outstanding risk to the intermediary is

Answer 13

normally collateralised
with securities,
minimising the default risk – t
hese securities are deposited with the intermediary and
retained in the event of default by the counterparty.

Question 14

warehousing swaps:

Answer 14

In practice, it is unlikely that two companies 
will contact an intermediary 
at the same time and want 
to take opposite positions 
in exactly the same swap. 
For this reason, a large financial institution will be prepared to 
enter into a swap 
without having an offsetting swap 
with another counterparty in place.

Question 15

Problems with warehousing swaps

Answer 15

bank should assess carefully
the risks it is taking on and
may decide to hedge them,
for example using appropriate forwards and futures.

Question 16

Valuing an interest rate swap

Answer 16

1. If we assume no possibility of default
   (which is reasonable when collateralised),
   an interest rate swap can be valued
   as a long position in one bond
   compared to a short position in another bond,
   since the notional principal is the same in both cases.
2. Alternatively, it can be valued
   as a portfolio of forward rate agreements.

Question 17

Variations on the vanilla interest rate swap include:

Answer 17

1 zero coupon swaps
⁃ (where each individual payment
⁃ under the par swap
⁃ is traded separately) 


2 amortising swaps
⁃ (where the principal
⁃ reduces in a predetermined way) 


3 step-up swaps
⁃ (where the principal increases
⁃ in a predetermined way) 


4 deferred swaps or forward swaps
⁃ (where the swap does not commence immediately and
⁃ so the parties do not begin to exchange interest payments
⁃ until some future date) 


Question 18

constant maturity swaps: CMs

Answer 18

where the floating leg of the swap is
for a longer maturity than
the frequency of payments). 
Whereas in a vanilla interest rate swap
the floating leg might be a 6-month interest rate paid,
and reset, every 6 months,
in a CMS
the floating leg might be
a 5-year market interest rate
but paid, and reset
to current market levels, every 6 months. 
The duration of the fixed flows
under the swap remains constant
during the swap’s life). 
For example,
imagine a UK investor believes that
the difference between the 6-month LIBOR rate
will fall relative to the 3-year swap rate for £ sterling.
To take advantage of this, the investor can buy a CMS,
paying the 6-month LIBOR rate
and receiving the 3-year swap rate.

Question 19

extendable swaps

Answer 19

where one party has the option to
extend the life of the swap
beyond a specified period) 


Question 20

puttable swaps

Answer 20

(where one party has
the option to terminate the swap
early).

Question 21

zero coupon swaps are

Answer 21

he most widely used variation by institutional investors
as they allow more precise hedging
of interest rate risk
than par swaps alone would permit.

Question 22

Currency swaps 


Answer 22

exchanging principal and interest payments
in one currency
for principal and interest payments in another currency.

This requires that
a principal be specified
n each of the two currencies –

these are usually chosen to be
approximately equivalent
using the exchange rate at the time the swap is initiated.

The principal amounts are
usually exchanged at the beginning and
at the end of the life of the swap –

as the companies involved
normally want to borrow the actual currencies. 


Question 23

a currency swap can be used to

Answer 23

transform borrowings in one currency into
borrowings in another currency.
It can also be used to transform the nature of assets.

Question 24

the currency swap can be valued as

Answer 24

(in the absence of default risk) 
as a position in two bonds. 
The value can therefore be determined from interest rates 
in the two currencies and 
the spot exchange rate.

Question 25

Total return swaps

Answer 25

following the growth in structured products
and exchange traded fund markets,

total return swaps have become commonplace.

The most common approach is for
the receiver to receive
the total return on a reference asset,

in return for paying
the reference floating rate
(eg 3 month LIBOR) plus or minus an adjustment.

The adjustment will allow for 
the net effect of 
hedging costs, 
inancing costs and 
dealing spreads.

Question 26

Total return swaps are available on

Answer 26

a wide range of 
equity, 
credit, 
interest rate, 
currency and 
commodity assets.

Question 27

RPI and LPI swaps

Answer 27

(swapping fixed rate for “index” return)

Question 28

An RPI swap

Answer 28

⁃ links one set of payments

⁃ to the level of the retail price index (RPI).

Question 29

⁃ Under an LPI (limited price indexation) swap

Answer 29

⁃ the payments are again linked to the RPI,
⁃ but capped at a maximum rate,
⁃ which is normally set at between 0% and 5% pa.

Question 30

cross-currency swaps or currency coupon swaps

Answer 30

⁃ (exchanging a fixed interest rate in one currency
⁃ for a floating interest rate in another currency.
⁃ This is a combination of
⁃ an interest rate swap and
⁃ a currency swap. )

Question 31

Dividend swaps

Answer 31

⁃ (Exchanging the dividends received
⁃ on a reference pool of equities
⁃ in return for a fixed rate). 


Question 32

Variance or volatility swaps

Answer 32

⁃ (Exchanging a fixed rate
⁃ in return for
⁃ the experienced variance or volatility of price changes
⁃ of a reference asset).

Question 33

Asset swaps

Answer 33

⁃ exchanging the fixed cashflows due
⁃ from a bond or other fixed income asset
⁃ in return for floating interest rates.

Question 34

commodity swaps

Answer 34

⁃ where one set of cashflows is exchanged for another
⁃ based on the current market price
⁃ of a particular commodity.

Question 35

different types of swap can be

Answer 35

combined in practice. 
So, it may be possible to 
enter into an 
extendable equity swap or 
an amortising LPI swap.

Question 36

Swaptions provide

Answer 36

one party with the right to enter into a certain swap

at a certain time in the future.

Question 37

Suppose a company knows that: 
		 in 1 year’s time it will be 
	⁃	entering an agreement to borrow 
	⁃	at a floating rate of interest 
	⁃	over a 3-year period 


Answer 37

 it will want to
⁃ swap the floating interest payments
⁃ for a series of fixed interest rate payments.
⁃ It could enter into a swaption
⁃ (by paying a premium now)
⁃ which gives it the option to
⁃ receive LIBOR
⁃ in return for paying, say, 5% pa fixed
⁃ for a 3-year period
⁃ starting in 1 year’s time.
⁃ If in a year’s time
⁃ the fixed rate that can be paid
⁃ in exchange for receiving LIBOR
⁃ within a 3-year swap
⁃ is greater than 5% pa,
⁃ then it will choose to exercise the swaption and
⁃ obtain the swap on more favourable terms
⁃ than those then available in the market
⁃ at that time.
⁃ If instead
⁃ the fixed rate turns out to be less than 5% pa,
⁃ then it will choose not to exercise the swaption and
⁃ will instead obtain the swap
⁃ on more favourable current market terms.

Question 38

first use of a swaption can be used to

Answer 38

provide companies 
with a guarantee that 
the fixed rate of interest 
they will pay on a loan at some future time 
will not exceed some level. 
The company is able to benefit from 
favourable interest rate movements 
while acquiring protection from unfavourable variations. 
This can be particularly useful for 
insurers 
wishing to offer policyholders 
the option of a fixed rate product (eg guaranteed annuity options).

Question 39

Equally, swaptions can be used to : second use of a swaption

Answer 39

place a limit on a floating rate, 
by providing the company 
with the option 
to swap that floating rate 
for a fixed rate.

Question 40

Swaptions are normally classified into three types, European, American and Bermudan.

Answer 40

1 A European swaption
⁃ gives the holder the right, but not the obligation,
⁃ to enter into a swap at the strike rate at a fixed expiry date in the future. 


2 An American swaption gives the holder the right, but not the obligation,
⁃ to enter into a swap at the strike rate at any date up to the expiry date. 


3 A Bermudan swaption gives the holder the right, but not the obligation, to enter into a swap at the strike rate
⁃ at multiple fixed dates.

Question 41

interest rate swap can be thought of as

Answer 41

an agreement to swap a fixed-rate bond 
for a floating-rate bond. 
Furthermore it can be shown that 
at the start of a swap, 
the value of the floating-rate bond is 
always equal 
to the principal amount of the swap

Question 42

A swaption can be regarded as

Answer 42

an option to exchange 
a fixed-rate bond for 
the principal amount of the swap – 
a put option in the case of paying fixed and receiving floating, 
a call option in the other direction.

Question 43

a swaption is an example of a more general class of

Answer 43

bond option – 
options to buy (or sell) a particular bond 
by a certain date 
for a particular price. 
Such contracts may be 
traded separately or 
may be embedded into conventional bonds 
to create puttable or callable bonds. 
Separate trading: allows the holder to demand early redemption at a predetermined price at certain times in the future, 
while embedding allows the issuing firm to 
buy back the bond 
at a predetermined price 
at certain times in the future.

Question 44

A callable bond is not

Answer 44

normally callable during the first few years of its life.
Thereafter the predetermined strike price
of a callable bond is
usually a decreasing function of term.
Thus, the issuer might first be able to redeem the bond at a price of 112 after 5 years, 110 after 6 years, 108 after 7 years and so on.

Question 45

A callable bond will generally offer

Answer 45

a higher yield than
an otherwise identical bond with no option features,
whereas the reverse is true
of a puttable bond. 


Question 46

Why is a swaption equivalent to a put option in the case of paying fixed and receiving floating?

Answer 46

case of a swaption, which gives you
the option to pay fixed and receive floating.

If you include the notional principal,
then the paying fixed side of the swap is the equivalent of selling a fixed interest bond to the other party
(ie they pay you a principal now and in return you pay a series of fixed interest payments and return the principal at the end of the term).

Similarly, the receiving floating side is equivalent to
buying a floating rate bond
(ie you pay a principal now and in return you receive a series of floating interest payments and also the principal back at the end of the term).

Question 47

the value of a floating rate bond on the day it is issued is

Answer 47

always simply equal to the amount of the principal.
(Intuitively this is because
our best estimates of the future variable payments are based on
the current pattern of forward rates,
which are also used to discount those same payments.
Thus, although any increase in future rates is consistent with higher expected future cashflows,
it also means that those cashflows are discounted more heavily in order to calculate their present value. )
Thus, the present value of the floating rate bond payments we receive
is simply equal to the principal amount.
Hence, in entering the swap
we have effectively agreed to sell a fixed interest bond in return for the principal amount of the (floating rate) bond.
A swaption therefore gives us
the option to effectively sell a fixed interest bond in return for the principal amount of the (floating rate) bond and
so is equivalent to a put option on a fixed interest bond.
The same argument applies in reverse
for a call option.

Question 48

loan and deposit instruments can also contain

Answer 48

embedded options – 
for example, prepayment provisions on 
loans and mortgages.
 are effectively call options on bonds because 
they give the borrower the right to 
buy back the loan from the lender.

Question 49

Forwards For currencies

Answer 49

the simplest form of derivative contract –
an agreement to buy (or sell) an asset
at a certain future time for a certain price.
traded in the over-the-counter market, and
are commonly used to hedge foreign currency risk.

Question 50

Although a forward contract is OTC,

Answer 50

once the contract is agreed
it is often migrated to a Central Clearing Party (CCP),
which means that margin payments are collected from both parties
in the same way as they would be for a (standardised) futures contract.

Question 51

The price in a forward contract is known as

Answer 51

the delivery price.
It is chosen so that
the value of the forward contract to both sides
is zero at the time it is entered into.

Question 52

Forwards also exist in respect of interest rates – a forward-rate agreement (FRA) is a forward contract where

Answer 52

the parties agree that a certain interest rate will apply to
a certain principal amount
during a specified future time period.

Thus, an interest rate swap can be
regarded
as a portfolio of forward-rate agreements.

Equally, a currency swap can be
decomposed into a series of forward contracts.

Question 53

while swaps will usually be constructed to have zero initial value

Answer 53

this does not mean that
each of the individual forward contracts underlying the swap
also has zero value –
rather, some will have positive and
some negative expected values.
This is important when the
credit risk in the swap is being evaluated.

Question 54

if the term structure of interest rates slopes downward at the time the swap is agreed

Answer 54

then the later forward rates must be
lower than the earlier ones.
Thus, given that the total value of the FRAs is zero,
the values of the later FRAs must be positive for A
and the values of the earlier FRAs must be negative. 


Question 55

How would the values of the FRAs vary for Company B if the term structure of interest rates was upward-sloping?

Answer 55

Hence, if the term structure of interest rates slopes upward at the time the swap is agreed
then the later forward rates must be higher than the earlier ones.
Thus, given that the total value of the FRAs is zero,
the values of the later FRAs must be positive for B
and the values of the earlier FRAs must be negative.