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1、10BinomialOptionPricing:BasicConceptsInearlierchapterswediscussedhowthepriceofoneoptionisrelatedtothepriceofanother,butwedidnotexplainhowtodeterminethepriceofanoptionrelativetothepriceoftheunderlyingasset.Inthischapterwediscussthebinomialoptionpricingmodel,withwhichwecancomputethepriceo
2、fanoption,giventhecharacteristicsofthestockorotherunderlyingasset.Thebinomialoptionpricingmodelassumesthat,overaperiodoftime,thepriceoftheunderlyingassetcanmoveupordownonlybyaspecifiedamount—thatis,theassetpricefollowsabinomialdistribution.Giventhisassumption,itispossibletodetermineano-a
3、rbitragepricefortheoption.Surprisingly,thisapproach,whichappearsatfirstglancetobeoverlysimplistic,canbeusedtopriceoptions,anditconveysmuchoftheintuitionunderlyingmorecomplex(andseeminglymorerealistic)optionpricingmodelsthatwewillencounterinlaterchapters.Itishardtooverstatethevalueofthoro
4、ughlyunderstandingthebinomialapproachtopricingoptions.Becauseofitsusefulness,wedevotethisandthenextchaptertobinomialoptionpricing.Inthischapter,wewillseehowthebinomialmodelworksanduseittopricebothEuropeanandAmericancallandputoptionsonstocks,currencies,andfuturescontracts.Aspartofthepric
5、inganalysis,wewillalsoseehowmarket-makerscancreateoptionssyntheticallyusingtheunderlyingassetandrisk-freebonds.Inthenextchapter,wewillexploreaspectsofthemodelinmoredepth.10.1AONE-PERIODBINOMIALTREEBinomialpricingachievesitssimplicitybymakingaverystrongassumptionaboutthestockprice:Atanyp
6、ointintime,thestockpricecanchangetoeitheranupvalueoradownvalue.In-between,greaterorlesservaluesarenotpermitted.Therestrictiontotwopossiblepricesiswhythemethodiscalled“binomial.”Theappealofbinomialpricingisthatitdisplaysthelogicofoptionpricinginasimplesetting,usingonlyalgebratopriceoptio
7、ns.ThebinomialapproachtopricingwasfirstusedbySharpe(1978)asanintuitivewaytoexplainoptionpricing.BinomialpricingwasdevelopedmoreformallybyCoxetal.(1979)andRendlemanandBartter(1979),whoshowedhowtoimplementthemodel,demonstratedthelinkbetweenthebinomialmodelandtheBlack-Scholesmodel,
