Flashcards in swap variations Deck (55):

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