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1

A swap is

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).

2

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

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.

3

For swaps note that

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. 


4

What is LIBOR?

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.

5

A series of LIBOR rates exists for different terms

(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.

6

LIBOR zero rates are generally

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

7

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

LIBOR rates.

8

cashflows under a “plain vanilla” swap.

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.

9

Using a swap to transform the nature of the liabilities

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.

10

swaps can be used to transform the nature of an asset

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

11

Arranging a swap

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.

12

Interest rate swap with a bank as intermediary example

  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.

13

In practice, any outstanding risk to the intermediary is

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.

14

warehousing swaps:

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.

15

Problems with warehousing swaps

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

16

Valuing an interest rate swap

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.

17

Variations on the vanilla interest rate swap include:

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) 


18

constant maturity swaps: CMs

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.

19

extendable swaps

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


20

puttable swaps

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

21

zero coupon swaps are

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

22

Currency swaps 


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. 


23

a currency swap can be used to

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

24

the currency swap can be valued as

(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.

25

Total return swaps

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.

26

Total return swaps are available on

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

27

RPI and LPI swaps

(swapping fixed rate for “index” return)

28

An RPI swap

⁃ links one set of payments
⁃ to the level of the retail price index (RPI).

29

⁃ Under an LPI (limited price indexation) swap

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

30

cross-currency swaps or currency coupon swaps

⁃ (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. )

31

Dividend swaps

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


32

Variance or volatility swaps

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

33

 Asset swaps

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

34

commodity swaps

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

35

different types of swap can be

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

36

Swaptions provide

one party with the right to enter into a certain swap
at a certain time in the future.

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 


  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.

38

first use of a swaption can be used to

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).

39

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

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

40

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

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.

41

interest rate swap can be thought of as

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

42

A swaption can be regarded as

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.

43

a swaption is an example of a more general class of

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.

44

A callable bond is not

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.

45

A callable bond will generally offer

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


46

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

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).

47

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

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.

48

loan and deposit instruments can also contain

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.

49

Forwards For currencies

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.

50

Although a forward contract is OTC,

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.

51

The price in a forward contract is known as

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.

52

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

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.

53

while swaps will usually be constructed to have zero initial value

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.

54

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

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. 


55

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

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.