Alumno Options

8/10/2019 Alumno Options

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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

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desembolsaelpremioelegirloquemsconvenga,yen

faltasiempre

puede

dejar

de

elegir

lo

que

desea

Hayamarrasqueaseguranlosestragosyncoras

queresistenlasborrascas.Dadopsies ysabrisel

lmitedelaprdida,pudiendoexcederlagananciaala

fantasaysermayoranelaumentoquela

esperanza


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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


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ShortCall(Figure9.3,page213)

ProfitfromwritingoneEuropeancalloption:optionprice=$5,

s r epr ce=

10

05

70 80 90 100

110 120 130

Profit($)

Terminal

stockprice($)



John C. Hull 2013

30

20

5

PutOption

Isacontractthatgivestheholdertheright,

butnottheobligation,tosellacertainassetat

,

independentlyoftheassetprice(S).


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LongPut(Figure9.2,page213)

ProfitfrombuyingaEuropeanputoption:optionprice=$7,

strikeprice=$70

30

20

10

Profit($)

Terminal



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($)



John C. Hull 2013

30

20

8


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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


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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


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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


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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


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UnderstandingBSMFormula(CallOption)Increasein.


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


UnderstandingBSMFormula

(CallOption)IncreaseinT.


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



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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


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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)


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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


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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



John C. Hull 2013

Futures

26


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SpecificationofExchangeTradedOptions

x p a on a e

Strikeprice

EuropeanorAmerican

Callor

Put

(option

class)



John C. Hull 2013

27

MarketMakers

Mostexchangesusemarketmakersto

ac tateopt onstra ng

Amarketmakerquotesbothbidandask

priceswhenrequested

Themarketmakerdoesnotknowwhetherthe



John C. Hull 2013

orsell

28


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Margin(Page222224)

Marginisrequiredwhenoptionsaresold

Forexample,whenanakedcalloptioniswritteninthe

US,themarginisthegreaterof:

1 Atotalof100%oftheproceedsofthesaleplus20%

oftheunderlyingsharepricelesstheamount(ifany)

bywhichtheoptionisoutofthemoney

2 Atotalof100%oftheproceedsofthesaleplus10%

oftheunderlyingshareprice



John C. Hull 2013

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Warrants

Warrantsareoptionsthatareissuedby

a corporationorafinancialinstitution

Thenumberofwarrantsoutstandingis

determinedbythesizeoftheoriginal

issueand changesonlywhentheyare



John C. Hull 2013

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Warrants(continued)

Theissuersettlesupwiththeholder

w enawarrant sexerc se

Whencallwarrantsareissuedbya

corporationonitsownstock,exercise

willusuallyleadtonewtreasurystock

bein issued



John C. Hull 2013

31

EmployeeStockOptions(seealsoChapter14)

Employeestockoptionsareaformofremuneration

ssue yacompanyto tsexecut ves

Theyareusuallyatthemoneywhenissued

Whenoptions are exercisedthecompanyissues

morestockandsellsittotheoptionholderforthestrikeprice

Expensedontheincomestatement



John C. Hull 2013

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ConvertibleBonds

Convertiblebondsareregularbondsthat

timesinthefutureaccordingtoapredeterminedexchangeratio

Usuallyaconvertibleiscallable

Thecallprovisionisawayinwhichtheissuercan orceconversionatatimeearlierthantheholdermightotherwisechoose



John C. Hull 2013

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Warrants

arran sareop ons a are ssue or

written)bya corporationorafinancial

institution

Thenumberofwarrantsoutstandingisdeterminedbythesizeoftheoriginalissue&



John C. Hull 2013

changesonlywhentheyareexercisedor

whentheyexpire

34


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Warrants(continued)

Warrantsaretradedinthesamewa asstocks

Theissuersettlesupwiththeholderwhenawarrantisexercised

Whencall

warrants

are

issued

by

a



John C. Hull 2013

,leadtonewtreasurystockbeingissued

35

ExecutiveStockOptions

Optionissuedbyacompanytoexecutives

Whentheoptionisexercisedthecompany

issuesmorestock

Usuallyatthemoneywhenissued



John C. Hull 2013

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ConvertibleBonds

Convertiblebondsareregularbondsthat

canbeexchangedforequityatcertain

timesinthefutureaccordingtoa

predeterminedexchangeratio



John C. Hull 2013

37

ConvertibleBonds(continued)

Thecallprovisionisawayinwhichthe

issuercanforceconversionatatimeearlier

thantheholdermightotherwisechoose



John C. Hull 2013

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