Knock-out Kick-in options

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1、Knock-OutandKick-InCallOptionsMATH414–MathematicsofDerivativeSecuritiesFinalProjectMay5,2000DanielE.EmmeneggerKnock-OutandKick-InCallOptionsThepayoffofastandardEuropeanstyleoptionisbasedonthepriceoftheunderlyingassetontheexpirationdateoftheoptionandtheoption’sstrike(orexercise)price.Sincei

2、tdoesnotmatterwhatpaththeunderlyingassettakesduringthelifeoftheoption,thestandardEuropeancallorputoption–oftenalsoreferredtoas‘plainvanilla’option–ispath-independent.Derivativeswithamorecomplicatedpayoffstructurethanplainvanillaoptionsarecalledexoticoptions.Exoticoptionsarenotextremelynew,

3、buttheyhavebecomeamoreandmoreattractivetoolforbothhedgersandspeculatorsonlyrecently.Mostexoticoptionsarepath-dependent,meaningthattheirpayoffisdependentonwhatpaththeunderlyingassettakesduringthelifeoftheoption.Therearemanytypesofexoticoptions;theonesdiscussedinthispaperarebarrieroptions.Si

4、ncethemostwidelyusedbarrieroptionsareonforeignexchangerates,Iwillusecurrencyexchangeratesastheunderlyingasset.TheconceptofbarrieroptionsThepayoffofabarrieroptiondependsonwhetherornotthecurrencyexchangeratereachesacertainlevel(barrier)duringacertainperiodoftime.Knock-outandkick-inoptionsare

5、twodifferenttypesofbarrieroptions.Aknock-outoptionstartslikeastandardoptionbutgetsknockedoutimmediatelyandceasestoexistiftheunderlyingexchangeratetradesatorbeyondthebarrierlevel.Forthisreason,thebarrierofaknock-outoptionisalsoreferredtoastheoutstrike.Akick-inoptionisinactiveatfirstbutkicks

6、inimmediatelyandbehaveslikeastandardoptioniftheunderlyingcurrencyratetradesatorbeyondthebarrierlevel.Thus,thebarrierofakick-inoptionisalsocalledtheinstrike.1Barrieroptionsareavailableasbothcallandputoptions.Iwillonlyexaminecalloptionsinthispaper.Conceptually,therearefourpossibletypesofbarr

7、iercalloptions,twoofwhichareknock-outoptionsandtwoofwhicharekick-inoptions:§Knock-out-Down-and-outcall:Theoutstrikeisbelowtheinitialexchangerate.Iftheexchangeratedropstoorbelowtheoutstrikerateduringthespecifiedtimeperiod,thecalloptionisimmediatelyterminated.-U