paul wilmott on quantitative finance transaction costs

《paul wilmott on quantitative finance transaction costs》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、CHAPTER48transactioncostsInthisChapter...•howtoallowfortransactioncostsinoptionprices•howeconomiesofscalework•avarietyofhedgingstrategiesandtheireffectsonoptionprices48.1INTRODUCTIONTransactioncostsarethecostsincurredinthebuyingandsellingoftheunderlying,relatedtothebid-offerspread.Th

2、eBlack–Scholesanalysisrequiresthecontinuousrebalancingofahedgedportfolio,andno‘friction’suchastransactioncostsinsuchrebalancing.Inpractice,thisassumptionisincorrect.Dependingontheunderlyingmarketinquestion,costsmayormaynotbeimportant.Inamarketwithhightransactioncosts,stocksinemerging

3、marketsforexample,itwillbetoocostlytorehedgefrequently.Inmoreliquidmarkets,govern-mentbondsinfirst-worldcountriesforexample,costsarelowandportfolioscanbehedgedoften.Ifcostsareimportantthenthiswillbeanimportantfactorinthebid-offerspreadinoptionprices.Themodelingoftransactioncostswasini

4、tiatedbyHayneLeland.Iwilldescribehismodelandthenasimplemodelfortransactioncosts,theHoggard–Whalley–Wilmottmodelfornon-vanillaoptionsandoptionportfolios,whichisbasedonLeland’shedgingstrategyandmodel.Thesemodelswillgiveussomeinsightintotheeffectofcostsonthepricesofoption.Duetothemathem

5、aticalcomplexityofthissubject,thelatterpartofthischapterisnecessarilyjustareviewofkeyresultswithlittleoftheunderlyingmathematicaltheory.Theinterestedreaderisreferredtotheoriginalpapersforfurtherdetails.48.2THEEFFECTOFCOSTSIntheBlack–Scholesanalysisweassumedthathedgingtookplacecontinu

6、ously.Inasense,wetakethelimitasthetimebetweenrehedgesgoestozero,δt→0.Wethereforefindourselvesrehedginganinfinitenumberoftimesuntilexpiry.Withabid-offerspreadontheunderlyingthecostofrehedgingleadstoinfinitetotaltransactioncosts.Clearly,evenwithdiscretehedgingtheconsequencesofthesecostsas

7、sociatedwithrehedgingareimportant.Differentpeoplehave784PartFiveadvancedtopicsdifferentlevelsoftransactioncosts;thereareeconomiesofscale,sothatthelargertheamountthatapersontrades,thelesssignificantarehiscosts.IncontrastwiththebasicBlack–Scholesmodel,wemayexpectthatthereisnouniqueoptio

8、nvalue.Inste