8/10/2019 Alumno Options
1/19
29/09/2013
1
MechanicsofOptionsMarkets
Chapter9
Fundamentals of Futures and Options Markets, 8th Ed, Ch 9, Copyright John C. Hull 2013 1
ConfusionofConfusions.
JosedelaVega,Amsterdam(1688)LlamronlelosFlamencosOpsie,derivadodelverbo
latino O tio O tionis ue si ni ica eleccin or
quedaraeleccindelquelodaelpoderpediro
entregarlapartidaalquelorecibe...puesdeseaelque
desembolsaelpremioelegirloquemsconvenga,yen
faltasiempre
puede
dejar
de
elegir
lo
que
desea
Hayamarrasqueaseguranlosestragosyncoras
queresistenlasborrascas.Dadopsies ysabrisel
lmitedelaprdida,pudiendoexcederlagananciaala
fantasaysermayoranelaumentoquela
esperanza
8/10/2019 Alumno Options
2/19
29/09/2013
2
CallOption Isacontractthatgivestheholdertheright,
butnottheobligation,tobuyacertainasset
timeindependentlyoftheassetprice(S).
LongCall(Figure9.1,Page212)
ProfitfrombuyingoneEuropeancalloption:optionprice=
,s r epr ce= .
30
20
Profit($)
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
0
5
70 80 90 100
110 120 130
erm na
stockprice($)
4
8/10/2019 Alumno Options
3/19
29/09/2013
3
ShortCall(Figure9.3,page213)
ProfitfromwritingoneEuropeancalloption:optionprice=$5,
s r epr ce=
10
05
70 80 90 100
110 120 130
Profit($)
Terminal
stockprice($)
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
30
20
5
PutOption
Isacontractthatgivestheholdertheright,
butnottheobligation,tosellacertainassetat
,
independentlyoftheassetprice(S).
8/10/2019 Alumno Options
4/19
29/09/2013
4
LongPut(Figure9.2,page213)
ProfitfrombuyingaEuropeanputoption:optionprice=$7,
strikeprice=$70
30
20
10
Profit($)
Terminal
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
0
770605040 80 90 100
stockprice($)
7
ShortPut(Figure9.4,page214)
ProfitfromwritingaEuropeanputoption:optionprice=$7,
s r epr ce=
10
7
0 70
605040
80 90 100
Profit($)Terminal
stockprice($)
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
30
20
8
8/10/2019 Alumno Options
5/19
29/09/2013
5
Europeanvs.AmericanOptions
Europeanoptionscanonlybeexercisedatthe
ma ur yo econ rac .
Americanoptionscanbeexercisedatanytime
untilthematurityofthecontract.
Out,AtandIntheMoneyOptions AcalloptionisOutofthemoneyifthepriceof
theasset(S)isbelowthestrike(K)priceoftheo tion.Ifweexercisetheo tionwewillincurinaloss.I.e.:S=100;K=120.(S K)=20
AcalloptionisAtthemoneyifthepriceofthe
assetisequaltothestrikeprice.Thegainofexercisingtheoptionis0. = = =. . .
AcalloptionisInthemoneyifthepriceoftheassetisgreaterthanthestrikeprice.Ifweexercisetheoptionwewillhaveagain.I.e.:S=140;K=120.(S K)=20
8/10/2019 Alumno Options
6/19
29/09/2013
6
OptionsValue
Long
Long
Callvalueatexpiration Max(SK;0)
Putvalue atexpiration Max(KS;0)
Callvaluetoday ertMax(SK;0)
Putvalue today ertMax(KS;0)
CallFinancialOption,
Intrinsicvs.Temporalvalue
oc
Price
$190 IBMPrice
$20
$10
TemporalValue
Premium=Temporal
+Intrinsic
ValuePremium=$10+$20
$170 Strike
Price
IntrinsicValue
=SK
8/10/2019 Alumno Options
7/19
29/09/2013
7
CallOption,Intrinsicvs.Temporalvalue
WhenS
TimeValue IntrinsicValue 0
IntrinsicValue
TimeValue,value.ValueofOptionality
Option
Price
MAXIMUM
VALUE
O K(Strike) ST(UnderlyingAsset)
Outofthemoney At themoney Inthemoney
TimeValueoftheOption
ThetwomostimportantfactorsinTimeValue:
Timetoexpiration,thebiggerthetimethebigger
thevalue.
Volatility,thebiggerthevolatilitythebiggerthe
value.4
4.5
5Price of a c all option vs. volatility
0 10 20 30 40 50 60 700
0.5
1
1.5
2
2.5
3
.
Volatility in %
Calloptionprice
8/10/2019 Alumno Options
8/19
29/09/2013
8
OptionsValue:BlackScholesMerton(BSM)Formula(Calloption)
1 2rT
C SN d Ke N d
Where: S:Underlyingassetprice(How
do
we
calculate
S
of
a
stock?)
K:Strikeprice
2
1
log2
Sr T
Kd
T
2
2
log2
Sr T
Kd
T
T:Timetomaturity(expiration)oftheoption
r:Riskfreerate
s:Volatilityofreturnsoftheunderlyingasset
N():CumulativedistributionfunctionoftheN(0,1)distribution.
UnderstandingBSMFormula
(CallOption) Roughlyspeaking,youcanthinkofN(d2)astheprobabilityof
exercisingtheoption,timesthepresentvalueofthestrikeprice(KertN(d2))
1
tobeifitdoesexpireinthemoneytimesthestockprice(SN(d1))
S 100 S 60 S 40
K 60 K 60 K 60
r 5% r 5% r 5%T = 50 days 0,13 yrs. T = 50 days 0,13 yrs. T = 50 days 0,13 yrs.
25% 25% 25%
In the Money At the Money Out of the Money
N() N() N()
d1 5,78 1,00 d1 0,12 0,55 d1 -4,38 0,00
d2 5,69 1,00 d2 0,03 0,51 d2 -4,47 0,00
SN(d1) 100,00 SN(d1) 32,80 SN(d1) 0,00
Ke-rT
N(d2) 59,61 Ke-rT
N(d2) 30,45 Ke-rT
N(d2) 0,00
Option Price 40,39 Option Price 2,35 Option Price 0,00
8/10/2019 Alumno Options
9/19
29/09/2013
9
UnderstandingBSMFormula(CallOption)Increasein.
In the Money At the Money Out of the Money
S 100 S 60 S 40
K 60 K 60 K 60
r 5% r 5% r 5%
T = 50 days 0,13 yrs. T = 50 days 0,13 yrs. T = 50 days 0,13 yrs.
50% 50% 50%
N() N() N()
d1 2,96 1,00 d1 0,13 0,55 d1 -2,12 0,02
d2 2,78 1,00 d2 -0,05 0,48 d2 -2,30 0,01
SN(d1) 99,85 SN(d1) 33,01 SN(d1) 0,68
Ke-rT
N(d2) 59,45 Ke-rT
N(d2) 28,52 Ke-rT
N(d2) 0,63
Option Price 40,40 Option Price 4,49 Option Price 0,04
UnderstandingBSMFormula
(CallOption)IncreaseinT.
In the Money At the Money Out of the Money
S 100 S 60 S 40
K 60 K 60 K 60
r 5% r 5% r 5%
T = 50 days 1 yrs. T = 50 days 1 yrs. T = 50 days 1 yrs.
25% 25% 25%
N() N() N()d1 2,37 0,99 d1 0,33 0,63 d1 -1,30 0,10
d2 2,12 0,98 d2 0,08 0,53 d2 -1,55 0,06
SN(d1) 99,11 SN(d1) 37,64 SN(d1) 3,89
Ke-rT
N(d2) 56,10 Ke-rT
N(d2) 30,24 Ke-rT
N(d2) 3,48
Option Price 43,01 Option Price 7,40 Option Price 0,42
8/10/2019 Alumno Options
10/19
29/09/2013
10
Othervaluationmethods
ApartfromBSMthereexistsomeother
:
BinomialmethodCox,RossandRubinstein(1979).
Themethodisverytransparentandcanbebetter
understandandexplainedthanBSM.
Monte
Carlo
simulation,
very
useful
because
we
dont
.
LongstaffandSchwartz(2001)forthevaluationof
americanoptions.Speciallyusedinthevaluationof
abandonoptions.
IsthereanOptimalValuationMethod?
Theanswerisyes,anddependsonlyonthe
pro ectweareana yz ng,an t eava a e
informationthatwehave.
Donotdependsontheexpectedresultofthe
calculationmethod.Because
8/10/2019 Alumno Options
11/19
29/09/2013
11
ExistConvergenceinthedifferentvaluationmethods
OntheleftwecanseetheconvergencebetweenBSMandMonteCarlomethods.
Ontheri htitscom aredtheBSMandBinomialmethods Hull .
ConvergencedemonstrationbetweenbinomialandregressionisdoneinSmith(2005)andBrandao,Dyer,Hahn(2005)
Naked positions.LongCall andshortcall
Beneficio de un inversor largo en call sob re Repsol a 25,00 con prim a 0,80
Repsol a 24 Repsol a 25 Repsol a 25,8 Repsol a 26
Compra Accin (25,00) (25,00) (25,00) (25,00)
Venta Accin 24,00 25,00 25,80 26,00
Prima de la Opcin (0,80) (0,80) (0,80) (0,80)
Resultado Terico (1,80) (0,80) 0,00 0,20
Beneficio
25
25,80
Outofthe
money
Athte
money
Inthe
money 0,80
2 5 2 5, 80
BeneficioLong Position Short Position
Decisin No Ejerce No Ejerce Ejerce Ejerce
Resultado Final (0,80) (0,80) 0,00 0,20
CotizacindelSubyacente(S)
0,80
CotizacindelSubyacente(S)
8/10/2019 Alumno Options
12/19
29/09/2013
12
Naked positions.LongPut andshortPut
Beneficio de un inversor largo en put sobr e Repsol a 25,00 con prim a 1,20
Rep sol a 23 Reps ol a 23,8 Reps ol a 25 Reps ol a 26
Compra Accin (23,00) (23,80) (25,00) (26,00)
Venta Accin 25,00 25,00 25,00 25,00
Gasto por Prima (1,20) (1,20) (1,20) (1,20)
Resultado Terico 0,80 0,00 (1,20) (2,20)
Decisin Ejerce Ejerce No Ejerce No Ejerce
i
Long Position Short Position
i , , , ,
1,20
25
2523,80
23,80
BeneficioBeneficio
Outofthe
money
Athte
money
Inthe
money
1,20
CotizacindelSubyacente(S) CotizacindelSubyacente(S)
Long Stock + Long Put
B
Resultsofthecombinationofthe
underlyingassetandanoption
Compra de 1.000 Acciones de BBVA a 17 y 10 Put (1/100) @ 18 . Prima 1,50
BBVA a 16 BBVA a 17 BBVA a 18 BBVA a 19 BBVA a 20
S
+
K
Long Stock + Short CallB
Resultado Acciones (1.000) 0 1.000 2.000 3.000
Prima Opcin ( 1.5 00 ) ( 1. 50 0) ( 1. 50 0) ( 1.5 00 ) ( 1. 500)
Decisin Ej erce Ejerce Ejerce N o Ejerce N o Ej erce
Resultado Put 2.000 1.000 0,00 0,00 0,00
Resultado Final (500) (500) (500) 500 1.500
+
K S
Compra de 1.000 Acciones de SAN a 12 y Venta de 10 Call (1/100) @ 13 . Prima 0,30
SAN a 11 SAN a 12 SAN a 13 SAN a 14 SAN a 15
Resultado Acciones (1.000) 0 1.000 2.000 3.000
Prima Opcin (300) (300) (300) (300) (300)
Resultado Call 0 0 0 (1.000) (2.000)
Resultado Final (1.300) (300) 700 700 700
8/10/2019 Alumno Options
13/19
29/09/2013
13
Long Stock + Long Put
B
+
Resultsofthe
combination
ofthe
underlying
assetandanoption.Summary
Short Stock + Long Call
B
+
S S
K
Long Stock + Short CallB
+
Short Stock + Short Put
K
B
S
K
SK
AssetsUnderlying
ExchangeTradedOptionsPage215216
Stocks
ForeignCurrency
StockIndices
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
Futures
26
8/10/2019 Alumno Options
14/19
29/09/2013
14
SpecificationofExchangeTradedOptions
x p a on a e
Strikeprice
EuropeanorAmerican
Callor
Put
(option
class)
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
27
MarketMakers
Mostexchangesusemarketmakersto
ac tateopt onstra ng
Amarketmakerquotesbothbidandask
priceswhenrequested
Themarketmakerdoesnotknowwhetherthe
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
orsell
28
8/10/2019 Alumno Options
15/19
29/09/2013
15
Margin(Page222224)
Marginisrequiredwhenoptionsaresold
Forexample,whenanakedcalloptioniswritteninthe
US,themarginisthegreaterof:
1 Atotalof100%oftheproceedsofthesaleplus20%
oftheunderlyingsharepricelesstheamount(ifany)
bywhichtheoptionisoutofthemoney
2 Atotalof100%oftheproceedsofthesaleplus10%
oftheunderlyingshareprice
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
29
Warrants
Warrantsareoptionsthatareissuedby
a corporationorafinancialinstitution
Thenumberofwarrantsoutstandingis
determinedbythesizeoftheoriginal
issueand changesonlywhentheyare
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
30
8/10/2019 Alumno Options
16/19
29/09/2013
16
Warrants(continued)
Theissuersettlesupwiththeholder
w enawarrant sexerc se
Whencallwarrantsareissuedbya
corporationonitsownstock,exercise
willusuallyleadtonewtreasurystock
bein issued
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
31
EmployeeStockOptions(seealsoChapter14)
Employeestockoptionsareaformofremuneration
ssue yacompanyto tsexecut ves
Theyareusuallyatthemoneywhenissued
Whenoptions are exercisedthecompanyissues
morestockandsellsittotheoptionholderforthestrikeprice
Expensedontheincomestatement
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
32
8/10/2019 Alumno Options
17/19
29/09/2013
17
ConvertibleBonds
Convertiblebondsareregularbondsthat
timesinthefutureaccordingtoapredeterminedexchangeratio
Usuallyaconvertibleiscallable
Thecallprovisionisawayinwhichtheissuercan orceconversionatatimeearlierthantheholdermightotherwisechoose
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
33
Warrants
arran sareop ons a are ssue or
written)bya corporationorafinancial
institution
Thenumberofwarrantsoutstandingisdeterminedbythesizeoftheoriginalissue&
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
changesonlywhentheyareexercisedor
whentheyexpire
34
8/10/2019 Alumno Options
18/19
29/09/2013
18
Warrants(continued)
Warrantsaretradedinthesamewa asstocks
Theissuersettlesupwiththeholderwhenawarrantisexercised
Whencall
warrants
are
issued
by
a
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
,leadtonewtreasurystockbeingissued
35
ExecutiveStockOptions
Optionissuedbyacompanytoexecutives
Whentheoptionisexercisedthecompany
issuesmorestock
Usuallyatthemoneywhenissued
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
36
8/10/2019 Alumno Options
19/19
29/09/2013
19
ConvertibleBonds
Convertiblebondsareregularbondsthat
canbeexchangedforequityatcertain
timesinthefutureaccordingtoa
predeterminedexchangeratio
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
37
ConvertibleBonds(continued)
Thecallprovisionisawayinwhichthe
issuercanforceconversionatatimeearlier
thantheholdermightotherwisechoose
Fundamentals of Futures and Options
Markets, 8th Ed, Ch 9, Copyright
John C. Hull 2013
38