资源描述：
《paul wilmott on quantitative finance barrier 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、CHAPTER23barrieroptionsInthisChapter...•thedifferenttypesofbarrieroptions•howtopricemanybarriercontractsinthepartialdifferentialequationframework•someofthepracticalproblemswiththepricingandhedgingofbarriers23.1INTRODUCTIONImentionedbarrieroptionsbrieflyinthepreviouschapte
2、r.Butinthischapterwestudythemindetail,frombothatheoreticalandapracticalperspective.Barrieroptionsarepath-dependentoptions.Theyhaveapayoffthatisdependentontherealizedassetpathviaitslevel;certainaspectsofthecontractaretriggerediftheassetpricebecomestoohighortoolow.Forexamp
3、le,anup-and-outcalloptionpaysofftheusualmax(S−E,0)atexpiryunlessatanytimepre-viouslytheunderlyingassethastradedatavalueSuorhigher.Inthisexample,iftheassetreachesthislevel(frombelow,obviously)thenitissaidto‘knockout,’becomingworthless.Apartfrom‘out’optionslikethis,therear
4、ealso‘in’optionswhichonlyreceiveapayoffifalevelisreached,otherwisetheyexpireworthless.Barrieroptionsarepopularforanumberofreasons.Perhapsthepurchaserusesthemtohedgeveryspecificcashflowswithsimilarproperties.Usually,thepurchaserhasverypreciseviewsaboutthedirectionofthemarke
5、t.Ifhewantsthepayofffromacalloptionbutdoesnotwanttopayforalltheupsidepotential,believingthattheupwardmovementoftheunderlyingwillbelimitedpriortoexpiry,thenhemaychoosetobuyanup-and-outcall.Itwillbecheaperthanasimilarvanillacall,sincetheupsideisseverelylimited.Ifheisrighta
6、ndthebarrierisnottriggeredhegetsthepayoffhewanted.Thecloserthatthebarrieristothecurrentassetpricethenthegreaterthelikelihoodoftheoptionbeingknockedout,andthusthecheaperthecontract.Conversely,an‘in’optionwillbeboughtbysomeonewhobelievesthatthebarrierlevelwillberealized.Ag
7、ain,theoptionischeaperthantheequivalentvanillaoption.386PartTwoexoticcontractsandpathdependency23.2DIFFERENTTYPESOFBARRIEROPTIONSTherearetwomaintypesofbarrieroption:•Theoutoption,thisonlypaysoffifalevelisnotreached.Ifthebarrierisreachedthentheoptionissaidtohaveknockedout
8、.•Theinoption,thispaysoffaslongasalevelisreachedbeforeexpiry.Ifthebarrierisreachedthentheoptionissaidto
