binomial option pricing _f-0943_

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1、DardenGraduateSchoolofBusinessAdministrationUVA-F-0943UniversityofVirginiaBINOMIALOPTIONPRICINGBinomialoptionpricingisasimplebutpowerfultechniquethatcanbeusedtosolvemanycomplexoption-pricingproblems.IncontrasttotheBlack-Scholesandothercomplexoption-pricingmodelsthatrequiresolutionstostocha

2、sticdifferentialequations,thebinomialoption-pricingmodel(two-stateoption-pricingmodel)ismathematicallysimple.Itisbasedontheassumptionofnoarbitrage.Theassumptionofnoarbitrageimpliesthatallrisk-freeinvestmentsearntherisk-freerateofreturnandnoinvestmentopportunitiesexistthatrequirezerodollars

3、ofinvestmentbutyieldpositivereturns.Itistheactivityofmanyindividualsoperatingwithinthecontextoffinancialmarketsthat,infact,upholdstheseconditions.Theactivitiesofarbitrageursorspeculatorsareoftenmalignedinthemedia,buttheiractivitiesinsurethatourfinancialmarketswork.Theyinsurethatfinancialas

4、setssuchasoptionsarepricedwithinanarrowtoleranceoftheirtheoreticalvalues.BINOMIALOPTION-PRICINGMODELAssumethatwehaveashareofstockwhosecurrentpriceis$100/share.Duringthenextmonth,thepriceofthestockiseithergoingtogoupto$110(upstate)orgodownto$90(downstate).Nootheroutcomesarepossibleoverthene

5、xtmonthforthisstock'sprice.BeginningValueEndofMonthValue$110$100$90____________________________________________________________________________________ThisnotewaspreparedbyProfessorRobertM.Conroy.Copyrightã2003bytheUniversityofVirginiaDardenSchoolFoundation,Charlottesville,VA.Allrightsrese

6、rved.Toordercopies,sendane-mailtodardencases@virginia.edu.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,usedinaspreadsheet,ortransmittedinanyformorbyanymeans—electronic,mechanical,photocopying,recording,orotherwise—withoutthepermissionoftheDardenSchoolFoundation.-2-UVA-F-

7、0943Nowassumethatacalloptionexistsonthisstock.Thecalloptionhasastrikepriceof$100andmaturesattheendofthemonth.Thevalueofthiscalloptionattheendofthemonthwillbe$10ifthestockpriceis$110and0ifthestockpriceis$90.Thepayoffatmaturity(onemonthfromnow)forthiscalloptioni