ch 15 hull fundamentals 8 the d

7/25/2019 Ch 15 Hull Fundamentals 8 the d

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull !"1#

Options on Stock Indicesand Currencies

Chapter 15

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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#

Index Options

The most popular indices underlying optionsin the U.S. are The S&P 100 Index (!" and "!#

The S&P 500 Index (SP"# The $o% ones Index times 0.01 ($"# The 'asda 100 Index ('$"#

Contracts are on 100 times index) they aresettled in cash) !" is *merican) the "!and all other options are !uropean.

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Index Option Example

Consider a call option on an index%ith a stri+e price o, 1-0

Suppose 1 contract is exercised%hen the index le/el is 1-0

hat is the payo,,2

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Using Index Options for Portfolio

Insurance Suppose the /alue o, the index is S0and the stri+e

price isK

I, a port,olio has a o, 1.03 the port,olio insuranceis o4tained 4y 4uying 1 put option contract on theindex ,or each 100S0dollars held

I, the is not 1.03 the port,olio manager 4uys

put options ,or each 100S0dollars held In 4oth cases3Kis chosen to gi/e the appropriate

insurance le/el

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Example 1

Port,olio has a 4eta o, 1.0 It is currently %orth 5003000

The index currently stands at 1000hat trade is necessary to pro/ide

insurance against the port,olio /alue

,alling 4elo% 65030002


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Example 2

Port,olio has a 4eta o, -.0 It is currently %orth 5003000 and index

stands at 1000The ris+7,ree rate is 1-8 per annumThe di/idend yield on 4oth the port,olio

and the index is 689o% many put option contracts should

4e purchased ,or port,olio insurance2

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I, index rises to 10603 it pro/ides a60:1000 or 68 return in ; months

Total return (incl. di/idends#


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%etermining t$e Strike Price &'a(le1)*2+ page ##,-

*n option %ith a stri+e price o, ?0 %ill pro/ide protectionagainst a 108 decline in the port,olio /alue

8

=alue o, Index in ;months

!xpected Port,olio =aluein ; months (#

1300 5@03000

13060 5;0300013000 6?03000 ?.0 6503000 ?-0 6103000

0 ;@03000


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Currenc. Options

Currency options trade on the '*S$*AB"

There also exists an acti/e o/er7the7counter

(TC# mar+et Currency options are used 4y corporations

to 4uy insurance %hen they ha/e an "

exposure

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Range /orward Contracts

9a/e the e,,ect o, ensuring that the exchangerate paid or recei/ed %ill lie %ithin a certainrange

hen currency is to 4e paid it in/ol/es selling aput %ith stri+eK1and 4uying a call %ith stri+eK-

hen currency is to 4e recei/ed it in/ol/es

4uying a put %ith stri+eK1and selling a call %ithstri+eK-

'ormally the price o, the put euals the price o,the call

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Range /orward Contract continued/igure 1)*1+ page ##0

Payo,,

*sset

PriceK1 K-

Payo,,

*ssetPrice

K1 K-

ShortPosition

DongPosition

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European Options on Stocks

wit$ nown %i!idend ields

e get the same pro4a4ilitydistri4ution ,or the stoc+ price at time

Tin each o, the ,ollo%ing casesE1. The stoc+ starts at price S0and

pro/ides a di/idend yield < q

-. The stoc+ starts at price S0eqT

andpro/ides no income

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European Options on Stocks

Pa.ing %i!idend ield

continued

e can /alue !uropean options 4y

reducing the stoc+ price to S0eqTand then4eha/ing as though there is no di/idend

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Extension of C$apter 13 Results&E4uations 1)*1 to 1)*#-

Do%er Found ,or callsE

Do%er Found ,or puts

Put Call Parity

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)0,max( 0rTqT

KeeSc

)0,max( 0qTrT eSKep

qTrTeSpKec

+=+ 0


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Extension of C$apter 1# Results&E4uations 1)*5 and 1)*)-

15

TTqrKSd

T

TqrKSd

dNeSdNKep

dNKedNeSc

qTrT

rTqT

+=

++=

=

=

)2/2

()/ln(

)2/2()/ln(

)()(

)()(

02

01

102

210

%here


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"aluing European Index Options

e can use the ,ormula ,or an optionon a stoc+ paying a continuous

di/idend yieldSet S0< current index le/el

Set q< a/erage di/idend yield

expected during the li,e o, the option

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Using /orward6/utures Index

Prices &e4uations 1)*, and 1)*7+ page #5#-


17

TddT

TKFd

dNFdKNep

dKN)N(d[Fec

eSF

rT

rT

Tqr

=

+=

=

=

=

12

20

1

102

210

)(00

2/)/ln(

)]()([

)](

Ethatso


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Implied %i!idend ields

rom !uropean calls and puts %ith the same stri+eprice and time to maturity

These ,ormulas allo% term structures o, di/idend yieldsto 4e

TC !uropean options are typically /alued using the,or%ard prices (!stimates o, qare not then reuired# *merican options reuire the di/idend yield term

structure


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0

ln1SKepc

Tq

rT

+=


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Currenc. Options8 '$e /oreign

Interest Rate

e denote the ,oreign interest rate 4y rfThe return measured in the domestic

currency ,rom in/esting in the ,oreigncurrency is rf times the /alue o, the

in/estment

This sho%s that the ,oreign currencypro/ides a yield at rate rf

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"aluing European Currenc. Options

e can use the ,ormula ,or an optionon a stoc+ paying a continuousdi/idend yield E

Set S0< current exchange rate

Set q = r

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/ormulas for European Currenc.

Options&E4uations 1)*0 and 1)*9 page #55-

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T

Tf

rrKS

d

T

Tf

rrKS

d

dNeSdNKep

dNKedNeSc

TrrT

rTTr

f

f

+

=

++

=

=

=

)2/2()/ln(

)2/2()/ln(

)()(

)()(

0

2

0

1

102

210

%here


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Using /orward6/utures Exc$ange

Rates

&E4uations 1)*13 and 1)*11+ page #5)-Using

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F S e r r Tf

0 0= ( )

Tdd

T

TKF

d

dNFdKNep

dKNdNFecrT

rT

=

+=

=

=

12

2

0

1

102

210

2/)/ln(

)]()([

)]()([


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'$e Binomial :odel for ;merican

Options

S0u

u

S0d

d

S0

p

(1Gp#

f = e-rt[pfu+(1$p)fd ]

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'$e Binomial :odelcontinued

24

currenciesfor

indicesfor

/1

)(

)(

trr

tqr

t

fea

ea

udeudu

dap

=

=

==

=

ch 15 hull fundamentals 8 the d

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