more about american options and related matters

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1、CHAPTER63moreaboutAmericanoptionsandrelatedmattersInthisChapter...•whysomepeoplemightexerciseAmericanoptionsatnon-optimaltimes•theeffectofnon-optimalexerciseontheprofitoftheoptionwriter63.1INTRODUCTIONIn1998DrHyungsokAhn,thenmypostdoctoralresearcheratOxfordUniversity,andIwr

2、oteapaperontheexerciseofAmericanoptions.InthischapterIreproducethepaperwithjustafewminorchanges.However,tostartwith,here’swhattheniceDerivativesWeekpublishedbyusonthesubjectofearlyexercise.1014PartFiveadvancedtopics63.2WHATDERIVATIVESWEEKPUBLISHED1999InstitutionalInvestor

3、Inc.(articlereproducedwithkindpermission)moreaboutAmericanoptionsandrelatedmattersChapter63101563.3HOLDTHESETHOUGHTSIdon’twantyoutogetthewrongideawhilereadingthissoIwantyoutokeepthefollowinginmind.•ThewriterisintheBlack–Scholesworld,includingnotransactioncosts.•Theoptionho

4、ldercan’tdeltahedge(whywouldhebuytheoptionifhecould?).•Theoptioncannotbesold,thinkofitasOTC.Thismeansthattheholdercannotclosehispositionotherthanbyexercising.63.4CHANGEOFNOTATIONSincethisistheoriginalpaperIhavekepttheoriginalnotation.Themaindifferencesare•ForStandsreadS•Fo

5、rv(t,s)readV(S,t)∂V•Forvtread∂t∂V•Forvsread∂S∂2V•Forvssread∂S2•ForKreadE63.5ANDFINALLY,THEPAPER...1016PartFiveadvancedtopicsOnTradingAmericanOptionsHyungsokAhnandPaulWilmottOCIAM,OxfordUniversityAbstract.Inthispaperweconsidertheeffectthatearlyexercisehasontheprofitofthewrit

6、erofanAmericanoption.TheAmericanoptioniscorrectlypricedintheBlack–Scholesframeworkassumingthattheholderexercisesattheworstpossibletimeforthewriter.Thisearlyexercisetimeisunique.Butwhyshouldtheholderexerciseatthistime?IftheholderoftheAmericanoptionwantstobotheliminateallris

7、kbydeltahedgingandmaximizehiswealththencertainlyheshouldexercisehere.Butifheisfollowingthisstrategywhydoeshebothertobuytheoption?Completemarketsmakepurchasingtheoptionunnecessary.Solet’sassumethatheisfollowingsomeotherstrategy,asheisfreetodo.Now,clearlyhewouldalwaysbebette

8、roffsellingtheoptionthanexercisingit,butwhatifthecontractisOTC,andhecanonlyclosehispositi