Two Period Binomial Option Pricing Model - Breaking Down ...

The two period binomial option pricing model is a very popular model that explains how to price stock options. Using an Excel spreadsheet, we can easily... Youarehere:Home1/Financetopics2/Derivativevaluation3/TwoPeriodBinomialOptionPricingModelTwoPeriodBinomialOptionPricingModel Thetwoperiodbinomialoptionpricingmodelisaverypopularmodelthatexplainshowtopricestockoptions.Themodelusesaso-calledbinomialmodel.Abinomialmodelisbasedontheideathat,overthenextperiod,thevalueofanassetcanbeequaltooneoftwopossiblevalues.Hence,thenamebinomial.Themodelcanbeusedforpricingamericanstyleoptions. Onthispage,wediscussthebinomialmodel,discussatwoperiodbinomialmodelexampleandfinallyimplementatwoperiodbinomialoptionpricingmodelcalculatorinExcel.Theworksheetisavailablefordownloadatthebottomofthepage. Binomialpricingmodelformulas Let’sfirstgooverthenecessaryformulas.There’sanumberofvariablesweneedtodefinefirst.WedefineS0asthecurrentspotpriceoftheasset,Uastheupmovefactor,Dasthedownmovefactor,S+asthepriceoftheassetwhenthere’sanupmoveandS-asthestockpricewhenthere’sadownmove.finally,piUandpiDaretherisk-neutralprobabilitiesofanupandadownmove.WedefinepiDas(1-piU). Theserisk-neutralprobabilitiesarenottheactualprobabilitiesoftheassetgongupordown.Instead,theyaredefinedasfollows    whererfistheannualriskfreerate. Next,let’sdiscusstheprocessthatwehavetofollowtocalculatethevalueofanoption. westartbycalculatingthepayoffatmaturity wecalculatetheexpectedvalueateachnodeastheprobability-weightedaverageofthepayoffsineachstate wediscounttheexpectedvaluebacktotodayattherisk-freerate Binomialtreeoptionpricingexample Let’sapplythemethodologyusinganexample.ThefollowingtableillustrateshowwecaneasilyapplyabinomialinterestratetreeoptionpricingtemplateinExcel.Thespreadsheetweusedcanbedownloadedatthebottomofthepage. Themodelcanalsobeusedforpricingamericanstyleoptionsbychangingthevalueoftheoptionbasedonwhetherornottheoptionwillbeexercised.Itisnecessarytouseabinomialinterestratetreeoranothersimulationmethodbecausenoclosed-formsolutionexists. Summary Wediscussedthetwo-periodbinomialmodelforpricingoptions.Oncewehavetherisk-neutralprobabilities,itisamatterofcalculatingtheexpectedvalueateachnodeanddiscountingbacktothepresentattherisk-freerate. Theabovetopicisrelatedtothefollowingsetoftopics: ArbitragepricingtheoryDerivativevaluationOptionvaluationBlackScholesoptionpricingmodelBinomialmodel WanttohaveanimplementationinExcel?DownloadtheExcelfile:TwoPeriodBinomialOptionPricingModelexample Pages Home Alternativeinvestments BehavioralFinance Bondvaluation Derivativevaluation Equityvaluation Financebasics ModernPortfolioTheory Performancemeasurement Riskmanagement ForexTrading PassiveInvesting TechnicalAnalysis Scrolltotop