ch 15 hull fundamentals 8 the d
TRANSCRIPT
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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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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
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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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
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
Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
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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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
I, index rises to 10603 it pro/ides a60:1000 or 68 return in ; months
Total return (incl. di/idends#
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
%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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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
Currenc. Options
Currency options trade on the '*S$*AB"
There also exists an acti/e o/er7the7counter
(TC# mar+et Currency options are used 4y corporations
to 4uy insurance %hen they ha/e an "
exposure
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
Range /orward Contracts
9a/e the e,,ect o, ensuring that the exchangerate paid or recei/ed %ill lie %ithin a certainrange
hen currency is to 4e paid it in/ol/es selling aput %ith stri+eK1and 4uying a call %ith stri+eK-
hen currency is to 4e recei/ed it in/ol/es
4uying a put %ith stri+eK1and selling a call %ithstri+eK-
'ormally the price o, the put euals the price o,the call
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
Range /orward Contract continued/igure 1)*1+ page ##0
Payo,,
*sset
PriceK1 K-
Payo,,
*ssetPrice
K1 K-
ShortPosition
DongPosition
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
European Options on Stocks
wit$ 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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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
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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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
Extension of C$apter 13 Results&E4uations 1)*1 to 1)*#-
Do%er Found ,or callsE
Do%er Found ,or puts
Put Call Parity
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)0,max( 0rTqT
KeeSc
)0,max( 0qTrT eSKep
qTrTeSpKec
+=+ 0
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
Extension of C$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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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
"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#-
Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
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
Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
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0
ln1SKepc
Tq
rT
+=
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
Currenc. Options8 '$e /oreign
Interest Rate
e denote the ,oreign interest rate 4y rfThe return measured in the domestic
currency ,rom in/esting in the ,oreigncurrency is rf times the /alue o, the
in/estment
This sho%s that the ,oreign currencypro/ides a yield at rate rf
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
"aluing European Currenc. Options
e can use the ,ormula ,or an optionon a stoc+ paying a continuousdi/idend yield E
Set S0< current exchange rate
Set q = r
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
/ormulas for European Currenc.
Options&E4uations 1)*0 and 1)*9 page #55-
21
T
Tf
rrKS
d
T
Tf
rrKS
d
dNeSdNKep
dNKedNeSc
TrrT
rTTr
f
f
+
=
++
=
=
=
)2/2()/ln(
)2/2()/ln(
)()(
)()(
0
2
0
1
102
210
%here
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
Using /orward6/utures Exc$ange
Rates
&E4uations 1)*13 and 1)*11+ page #5)-Using
22
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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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
'$e Binomial :odel for ;merican
Options
S0u
u
S0d
d
S0
p
(1Gp#
f = e-rt[pfu+(1$p)fd ]
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Fundamentals of Futures and Options Markets, 8th Ed, Ch 15, Copyright John C. ull!"1#
'$e Binomial :odelcontinued
24
currenciesfor
indicesfor
/1
)(
)(
trr
tqr
t
fea
ea
udeudu
dap
=
=
==
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