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页数:18页
时间:2018-02-10
《paul wilmott on quantitative finance asian options》由会员上传分享,免费在线阅读,更多相关内容在工程资料-天天文库。
1、CHAPTER25asianoptionsInthisChapter...•manytypesofAsianoptionwithapayoffthatdependsonanaverage•thedifferenttypesofaveragingofassetpricesthatareusedindefiningthepayoff•howtopricethesecontractsinthepartialdifferentialequationframework25.1INTRODUCTIONAsianoptionsgivetheholderapayo
2、ffthatdependsontheaveragepriceoftheunderlyingoversomeprescribedperiod.ThisaveragingoftheunderlyingcansignificantlyreducethepriceofanAsianoptioncomparedwithasimilarvanillacontract.Anythingthatreducestheup-frontpremiuminanoptioncontracttendstomakethemmorepopular.•Thevolatilityof
3、theaverageofastockpriceovertimeislessthanthevolatilityofthestock.ThisoftenresultsinthepriceofAsianoptionsbeinglessthanequivalentvanillaoptions.•Theaverageislessexposedtosuddencrashesorralliesinastockprice.Allisnotlostifyouownacallandthestockplummetsjustbeforeexpiration.•Theav
4、erageovertimeishardertomanipulatethanasinglestockprice.Asiansareofobvioususewitheasilymanipulated,thinlytradedunderlyings.•Theaveragerateoptionscanbeusedtolockinthepriceofacommodityoranexchangerateforthosewhohaveacontinualandfairlypredictableexposuretooneoftheseoverextendedpe
5、riods.•Endusersofcommoditiesorenergyareoftenexposedtoaveragepricesovertime,soAsianoptionsareofobviousappeal.(Asianoptionsareoftenconsideredtobethevanillasofthecrudeoilmarket.)Asianoptionsmightbeboughtbysomeonewithastreamofcashflowsinaforeigncurrency,duetosalesabroadforexample,
6、andwhowantstohedgeagainstfluctuationsintheexchangerate.TheAsiantailthatweseelaterisdesignedtoreduceexposuretosuddenmovementsintheunderlyingjustbeforeexpiry;somepensionschemeshavesuchafeature.Asianoptionswerefirstsuccessfullypricedin1987byDavidSpaughtonandMarkStandishofBankersTr
7、ust.TheywereinTokyowhentheydevelopedthefirstcommerciallyusedpricingformulaforoptionslinkedtotheaveragepriceofcrudeoil.Apartfromthat,theadjective‘Asian’hasnosignificance.428PartTwoexoticcontractsandpathdependencyInthischapterwefinddifferentialequationsforthevalueofawidevarietyofs
8、uchAsianoptions.Therearemanywaystodefinean‘average’oftheprice,andwebe
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