期權期貨及其他衍生品Ch07HullOFOD10thEdition

Chapter

7SwapsOptions,

Futures,

and

Other

Derivatives,

10th

Edition,

Copyright

?John

C.

Hull

20171Nature

of

SwapsOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

20172Aswap

is

an

agreement

to

exchangecash

flows

at

specified

future

timesaccording

to

certain

specified

rulesAn

Example

of

a

“Plain

Vanilla”

Intere

Rate

SwapOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

20173An

agreement

by

Apple

to

receive

6-monthLIBOR

&

pay

a

fixed

rate

of

3%

per

annumevery

6

months

for

3

years

on

a

notionalprincipal

of

$100

millionNext

slide

illustrates

cash

flows

that

couldoccur(Day

count

conventions

are

notconsidered)Cash

Flows

to

Apple(See

Table

7.1,

page

157Millions

of

Dollars--Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

20174LIBORFLOATINGFIXEDNetDateRateCash

FlowCash

FlowCash

FlowMar.

8,

20162.2%Sept.

8,

20162.8%+1.10–1.50–0.40Mar.

8,

20173.3%+1.40–1.50–0.10Sept.

8,

20173.5%+1.65–1.50+0.15Mar.

8,

20183.6%+1.75–1.50+0.25Sept.

8,

20183.9%+1.80–1.50+0.30Mar.

8,

20193.4%+1.95–1.50+0.45Typical

Uses

of

an

Interest

Rate

SwapConverting

a

liability

fromfixed

rate

to

floating

ratefloating

rate

to

fixed

rateConverting

an

investment

fromfixed

rate

to

floating

ratefloating

rate

to

fixed

rateOptions,

Futures,

and

Other

Derivatives,

10th

Edition,

Copyright

?John

C.

Hull

20175Interest

Rate

Swap

BetweenOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

20176CitiAppleApple

and

Citigroup

(Figure

7.1,

page

156)3.0%LIBORApple

Transforms

a

Liability

fromFloating

to

Fixed(Figure

7.2,

page

158)Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

20177CitiApple3.0%LIBORLIBOR+0.1%Interest

Rate

Swap

Between

Citigroup

and

Intel

(Figure

7.3,

page

159)CitiIntel2.97%LIBOROptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

20178Intel

Transforms

a

Liability

from

Fixed

to

Floating

(Figure

7.4,

page

159)CitiIntel2.97%LIBOR3.2%Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

20179Apple

Transforms

an

Asset

from

Fixed

to

Floating

(Figure

7.5,

page

159)CitiApple3.0%LIBOR2.7%Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201710Intel

Transforms

an

Asset

from

Floating

to

Fixed

(Figure

7.6,

page

160)CitiIntel2.97%LIBORLIBOR?0.2%Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201711Quotes

By

a

Swap

Market

Maker

(Table

7.3,

page

161)MaturityBid

(%)Offer

(%)Swap

Rate

(%)2

years2.552.582.5653

years2.973.002.9854

years3.153.193.1705

years3.263.303.2807

years3.403.443.42010

years3.483.523.500Options,

Futures,

and

Other

Derivatives,

10th

Edition,

Copyright

?John

C.

Hull

201712Day

CountOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201713A

day

count

convention

is

specified

for

fixedand

floating

paymentsFor

example,

LIBOR

is

likely

to

be

actual/360in

the

U.S.

because

LIBOR

is

a

moneymarket

rateConfirmationsOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201714Confirmations

specify

the

terms

of

a

transactioThe

International

Swaps

and

Derivatives

hasdeveloped

Master

Agreements

that

can

be

usedto

cover

all

agreements

between

twocounterpartiesCCPs

are

used

for

most

standard

swapsbetween

two

financial

institutionsThe

Comparative

Advantage

Argument(Table

7.4,

page

163)AAACorp

wants

to

borrow

floatingBBBCorpwantsto

borrow

fixedFixedFloatingAAACorp4.00%6-month

LIBOR

?

0.1%BBBCorp5.20%6-month

LIBOR

+

0.6%Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201715A

Swap

where

Companies

Trade

Directly

with

Each

Other

(Figure

7.7,

page

164)AAACorpBBBCorp4.35%LIBORLIBOR+0.6%4%Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201716The

Swap

when

a

Financial

Institution

(F.I.)

is

Involved(Figure

7.7,

page

164)Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201717AAACorpBBBCorp4.33%LIBORLIBOR+0.6%4%LIBOR4.37%F.I.Criticism

of

the

Comparative

Advantage

ArgumentOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201718The

4.0%

and

5.2%

rates

available

toAAACorp

and

BBBCorp

in

fixed

rate

marketsare

5-year

ratesThe

LIBOR?0.1%

and

LIBOR+0.6%

ratesavailable

in

the

floating

rate

market

are

six-month

ratesBBBCorp’s

fixed

rate

depends

on

the

spreadabove

LIBOR

it

borrows

at

in

the

futureValuation

of

an

Interest

Rate

SwapOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201719Initially

interest

rate

swaps

are

worthclose

tozeroAt

later

times

they

can

be

valued

as

a

portfolioof

forward

rate

agreements

(FRAs)The

procedure

is

toCalculate

LIBOR

forward

ratesCalculate

the

swap

cash

flows

that

will

occur

ifLIBOR

forward

rates

are

realizedDiscount

these

swap

cash

flows

at

OIS

ratesExample

7.1

(page

166)Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?

John

C.

Hull

201720Swap

involves

paying

3%

per

annum

and

receiving

LIBORevery

six

months

on

$100

millionSwap

has

15

months

remaining

(exchanges

in

3,

9,

and

1months)LIBOR

rate

applicable

to

exchange

in

3

months

wasdetermined

3

months

ago

and

is

2.9%Forward

LIBOR

rates

for

3-9

month

period

and

9-15

montperiods

are

3.429%

and

3.734%,

respectivelyOIS

zero

rates

for

maturities

of

3,

9,

and

15

months

ar2.8%,

3.2%,

and

3.4%,

respectivelyCalculations

($

million)Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201721Time(yrs)Fixedcash

flowFloatingcash

flowNet

cashflowDiscountfactorPV

of

netcash

flow0.25?1.5000+1.4500?0.05000.9930?0.04970.75?1.5000+1.7145+0.21450.9763+0.20941.25?1.5000+1.8672+0.36720.9584+0.3519+0.5117Value

of

swap

is

$0.5117

millionBootstrapping

LIBOR

forward

rates:

Example

7.2

(page

167)Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?

John

C.

Hull

2017226,12,18,

and

24

month

OIS

rates

are

3.8%,

4.3%,

4.6%,and

4.75%

respectively

with

cont.

comp.6-month

LIBOR

rate

is

4%

(sa

comp.)Suppose

forward

LIBOR

rates

for

6-12

and

12-18

monthshavealready

been

calculated

as

5%

and

5.5%,respectively

(sa

comp)The

two

year

swap

rate

is

5%The

next

step

is

to

calculate

the

LIBOR

forward

rate,

F,the18-24

month

period.Bootstrapping

LIBOR

forward

rates:

CalculationsOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?

John

C.

Hull

201723A

2-year

swap

where

5%

is

paid

and

LIBOR

is

receivedon

$100

is

worth

zero.Value

of

first

three

exchanges

are0.5×(0.04?

0.05)×100×e?0.038×0.5

=

?0.49060.5×(0.05

?

0.05)×100×e?0.043×1.0

=

00.5×(0.055

?

0.05)×100×e?0.046×1.5

=

+0.2333The

value

of

the

fourth

payment

must

be

+0.2573

so

thatthe

total

value

is

zero0.5×(F?0.05)×100×e?0.0475×2.0

=

0.2573F

=

0.05566

or

5.566%

per

annumAn

Example

of

a

Fixed-for-

Fixed

Currency

Swap

(Figure

7.10,

page

169)Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201724Five

year

agreement

by

BP

toPay3%

on

a

US

dollar

principal

of$15,000,000Receive

4%

on

a

sterling

principal

of￡10,000,000Exchange

of

PrincipalOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201725In

an

interest

rate

swap

theprincipal

is

not

exchangedIn

a

currency

swap

the

principal

isexchanged

at

the

beginning

andthe

end

of

the

swapThe

Cash

Flows

(Table

7.5,

page

170)Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201726DateDollar

Cash

Flows(millions)Sterling

cash

flow(millions)Feb

1,

2016+15.00?10.00Feb

1,

2017?0.45+0.40Feb

1,

2018?0.45+0.40Feb

1,

2019?0.45+0.40Feb

1,

2020?0.45+0.40Feb

1,

2021?15.45+10.40Typical

Uses

of

a

Currency

SwapConversion

from

a

liability

in

one

currencyto

a

liability

in

another

currencyConversion

from

an

investment

in

onecurrency

to

an

investment

in

anothercurrencyOptions,

Futures,

and

Other

Derivatives,

10th

Edition,

Copyright

?John

C.

Hull

201727Comparative

Advantage

May

Be

Real

Because

of

TaxesOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201728General

Electric

wants

to

borrow

AUDQuantas

wants

to

borrow

USDBorrowing

costs

after

adjusting

for

thedifferential

impact

of

taxes

could

be:USDAUDGeneral

Electric5.0%7.6%Quantas7.0%8.0%Valuation

of

Fixed-for-Fixed

Currency

SwapsOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201729Fixed

for

fixed

currency

swaps

can

bevalued

either

using

forward

rates

or

asthe

difference

between

2

bondsExamples

7.3

and

7.4

(pages

172-174)Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201730All

Japanese

interest

rates

are

1.5%

per

annum

(contcomp.)All

USD

interest

rates

are

2.5%

per

annum

(cont.comp.)3%

is

received

in

yen;

4%

is

paid

in

dollars.Payments

are

made

annuallyPrincipals

are

$10

million

and

1,200

million

yenSwap

will

last

for

3

more

yearsCurrent

exchange

rate

is

110

yen

per

dollarValuation

in

Terms

of

Forward

Rates

(page

173)Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201731TimeDollarCashFlowYencashflowForwardrateDollar

valueof

yen

cashflowNet

cashflowPresentvalue1?0.4+360.0091820.3306?0.0694?0.06772?0.4+360.0092750.3339?0.0661?0.06293?10.4+12360.00936811.5786+1.1786+1.0934Total+0.9629Valuation

in

Terms

of

Bonds(page

174)Options,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201732TimeCash

Flows($

millions)PV($

millions)Cash

flows(millions

of

yen)PV

(

millionsof

yen)10.40.39013635.4620.40.38053634.94310.49.64851,2361,181.61Total10.41911,252.01Value

=

1,252.01/110?10.4191

=

+0.9629

millionsof

dollarsOther

Currency

SwapsOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201733Fixed-for-floating:

equivalent

to

a

fixed-forfixed

currency

swap

plus

a

fixed

for

floatinginterest

rate

swapFloating-for-floating:

equivalent

to

a

fixed-fixed

currency

swap

plus

two

floating

interestrate

swapsSwaps

&

ForwardsOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright

?JohnC.

Hull

201734Aswap

can

be

regarded

as

a

convenient

wayof

packaging

forward

contractsWhen

a

swap

is

initiated

the

swap

has

zerovalue,

but

typically

some

forwards

have

apositive

value

and

some

have

a

negativevalueCredit

RiskOptions,

Futures,

and

Other

Derivatives,

10th

Edition,Copyright