Binomial Option Pricing Model Definition - Investopedia

Real-World Example of Binomial Option Pricing Model · Cost today = $50 - option price · Portfolio value (up state) = $55 - max ($110 - $100, 0) = $45 · Portfolio ... Options&DerivativesTrading OptionsTradingStrategy&Education PartOf OptionsTradingGuide ExploreTheGuide Overview BasicOptionsOverview Overview EssentialOptionsTradingGuide BasicsofOptionsProfitability BasicsOfOptionPrice KeyOptionsConcepts Overview CallOptionDefinition PutOptionDefinition StrikePrice ExpirationDate OptionPremium InTheMoney OutOfTheMoney ImpliedVolatility OptionsTradingStrategies Overview 10OptionsStrategiesToKnow CoveredCall MarriedPut CreditSpreadsvs.DebitSpreads Straddles Strangles IronCondors ButterflySpreads StockOptionAlternatives Overview ETFOptionsvs.IndexOptions OptionsOnFutures CurrencyOptions BondOptions AdvancedOptionsConcepts Overview OptionsGreeks BlackScholesModel BinomialOptionPricingModel VolatilitySkew UnderstandingSyntheticOptions TableofContents Expand BinomialOptionPricing BasicsoftheBinomialPricing Calculatingw/theBinomialModel RealWorldExample WhatIstheBinomialOptionPricingModel? Thebinomialoptionpricingmodelisanoptionsvaluationmethoddevelopedin1979.Thebinomialoptionpricingmodelusesaniterativeprocedure,allowingforthespecificationofnodes,orpointsintime,duringthetimespanbetweenthevaluationdateandtheoption'sexpirationdate. KeyTakeaways ThebinomialoptionpricingmodelvaluesoptionsusinganiterativeapproachutilizingmultipleperiodstovalueAmericanoptions.Withthemodel,therearetwopossibleoutcomeswitheachiteration—amoveuporamovedownthatfollowabinomialtree.Themodelisintuitiveandisusedmorefrequentlyinpracticethanthewell-knownBlack-Scholesmodel. Themodelreducespossibilitiesofpricechangesandremovesthepossibilityforarbitrage.Asimplifiedexampleofabinomialtreemightlooksomethinglikethis: ImagebyJulieBang©Investopedia 2020 BasicsoftheBinomialOptionPricingModel Withbinomialoptionpricemodels,theassumptionsarethattherearetwopossibleoutcomes—hence,thebinomialpartofthemodel.Withapricingmodel,thetwooutcomesareamoveup,oramovedown.Themajoradvantageofabinomialoptionpricingmodelisthatthey’remathematicallysimple.Yetthesemodelscanbecomecomplexinamulti-periodmodel. IncontrasttotheBlack-Scholesmodel,whichprovidesanumericalresultbasedoninputs,thebinomialmodelallowsforthecalculationoftheassetandtheoptionformultipleperiodsalongwiththerangeofpossibleresultsforeachperiod(seebelow). Theadvantageofthismulti-periodviewisthattheusercanvisualizethechangeinassetpricefromperiodtoperiodandevaluatetheoptionbasedondecisionsmadeatdifferentpointsintime.ForaU.S-based option,whichcanbeexercisedatanytimebeforethe expirationdate,thebinomialmodelcanprovideinsightastowhenexercisingtheoptionmaybeadvisableandwhenitshouldbeheldforlongerperiods.  Bylookingatthe binomialtree ofvalues,atradercandetermineinadvancewhenadecisiononan exercise mayoccur.Iftheoptionhasapositivevalue,thereisthepossibilityofexercisewhereas,iftheoptionhasavaluelessthanzero,itshouldbeheldforlongerperiods. CalculatingPricewiththeBinomialModel Thebasicmethodofcalculatingthebinomialoptionmodelistousethesameprobabilityeachperiod forsuccessandfailure untiltheoptionexpires.However,atradercanincorporatedifferentprobabilitiesforeachperiodbasedonnewinformationobtainedastimepasses. Abinomialtreeisausefultoolwhenpricing Americanoptions and embeddedoptions.Itssimplicityisitsadvantageanddisadvantageatthesametime.Thetreeiseasytomodeloutmechanically,buttheproblemliesinthepossiblevaluestheunderlyingassetcantakeinoneperiodoftime.Inabinomialtreemodel,theunderlyingassetcanonlybeworthexactlyoneoftwopossiblevalues,whichisnotrealistic,asassetscanbeworthanynumberofvalueswithinanygivenrange. Forexample,theremaybea50/50chancethattheunderlyingassetpricecanincreaseordecreaseby30percentinoneperiod.Forthesecondperiod,however,theprobabilitythattheunderlyingassetpricewillincreasemaygrowto70/30. Forexample,ifaninvestorisevaluatinganoilwell,thatinvestorisnotsurewhatthevalueofthatoilwellis,butthereisa50/50chancethatthepricewillgoup.If oilprices goupinPeriod1makingtheoilwellmorevaluableandthemarketfundamentalsnowpointtocontinuedincreasesinoilprices,theprobabilityoffurtherappreciationinpricemaynowbe70percent.Thebinomialmodelallowsforthisflexibility;theBlack-Scholesmodeldoesnot. ImagebyJulieBang©Investopedia 2020 Real-WorldExampleofBinomialOptionPricingModel Asimplifiedexampleofabinomialtreehasonlyonestep.Assumethereisastockthatispricedat$100pershare.Inonemonth,thepriceofthisstockwillgoupby$10orgodownby$10,creatingthissituation: Stockprice=$100Stockpriceinonemonth(upstate)=$110Stockpriceinonemonth(downstate)=$90 Next,assumethereisacalloptionavailableonthisstockthatexpiresinonemonthandhasastrikepriceof$100.Intheupstate,thiscalloptionisworth$10,andinthedownstate,itisworth$0.Thebinomialmodelcancalculatewhatthepriceofthecalloptionshouldbetoday. Forsimplificationpurposes,assumethataninvestorpurchasesone-halfshareofstockandwritesorsellsonecalloption.Thetotalinvestmenttodayisthepriceofhalfasharelessthepriceoftheoption,andthepossiblepayoffsattheendofthemonthare: Costtoday=$50-optionpricePortfoliovalue(upstate)=$55-max($110-$100,0)=$45Portfoliovalue(downstate)=$45-max($90-$100,0)=$45 Theportfoliopayoffisequalnomatterhowthestockpricemoves.Giventhisoutcome,assumingnoarbitrageopportunities,aninvestorshouldearntherisk-freerateoverthecourseofthemonth.Thecosttodaymustbeequaltothepayoffdiscountedattherisk-freerateforonemonth.Theequationtosolveisthus: Optionprice=$50-$45xe^(-risk-freeratexT),whereeisthemathematicalconstant2.7183. Assumingtherisk-freerateis3%peryear,andTequals0.0833(onedividedby12),thenthepriceofthecalloptiontodayis$5.11. ThebinomialoptionpricingmodelpresentstwoadvantagesforoptionsellersovertheBlack-Scholesmodel.Thefirstisitssimplicity,whichallowsforfewererrorsinthecommercialapplication.Thesecondisitsiterativeoperation,whichadjustspricesinatimelymannersoastoreducetheopportunityforbuyerstoexecutearbitragestrategies. Forexample,sinceitprovidesastreamofvaluationsforaderivativeforeachnodeinaspanoftime,itisusefulforvaluingderivativessuchasAmericanoptions—whichcanbeexecutedanytimebetweenthepurchasedateandexpirationdate.ItisalsomuchsimplerthanotherpricingmodelssuchastheBlack-Scholesmodel. CompareAccounts AdvertiserDisclosure × TheoffersthatappearinthistablearefrompartnershipsfromwhichInvestopediareceivescompensation.Thiscompensationmayimpacthowandwherelistingsappear.Investopediadoesnotincludealloffersavailableinthemarketplace. Provider Name Description PartOf OptionsTradingGuideGuide HowOptionsWorkforBuyersandSellers 1of29 TheEssentialOptionsTradingGuide 2of29 TheBasicsofOptionsProfitability 3of29 TheBasicsOfOptionPrices 4of29 WhatIsaCallOption? 5of29 PutOptionDefinition 6of29 WhatIsaStrikePrice? 7of29 ExpirationDate(Derivatives)Definition 8of29 OptionPremiumDefinition 9of29 HowInTheMoney(ITM)OptionsWork 10of29 OutoftheMoney(OTM)DefinitionandExample 11of29 HowImpliedVolatility(IV)HelpsYoutoBuyLowandSellHigh 12of29 10OptionsStrategiestoKnow 13of29 CoveredCallDefinition 14of29 MarriedPutDefinition 15of29 What'stheDifferenceBetweenaCreditSpreadandaDebitSpread? 16of29 HowtoUseaStraddleOptionsStrategy 17of29 WhicheverWayaStockMoves,AStrangleCanSqueezeOutaProfit 18of29 IronCondorDefinitionandExample 19of29 ButterflySpreadDefinition 20of29 ETFOptionsvs.IndexOptions:What'stheDifference? 21of29 OptionsOnFuturesDefinition 22of29 CurrencyOption 23of29 BondOption 24of29 GreeksDefinition 25of29 WhatIstheBlack-ScholesModel? 26of29 HowtheBinomialOptionPricingModelWorks 27of29 UnderstandingtheVolatilitySkew 28of29 UnderstandingSyntheticOptions 29of29 RelatedTerms WhatIsaLattice-BasedModel? Alattice-basedmodelisamodelusedtovaluederivatives;itusesabinomialtreetoshowdifferentpathsthepriceoftheunderlyingassetmaytake. more WhatIstheBlack-ScholesModel? TheBlack-Scholesmodelisamathematicalequationusedforpricingoptionscontractsandotherderivatives,usingtimeandothervariables. more TrinomialOptionPricingModelDefinition Thetrinomialoptionpricingmodelisanoptionpricingmodelincorporatingthreepossiblevaluesthatanunderlyingassetcanhaveinonetimeperiod. more WhatIstheGammaPricingModel? ThegammapricingmodelcalculatesthefairmarketvalueofaEuropean-styleoptionwhenthepriceoftheunderlyingassetdoesnotfollowanormaldistribution. more WhatIstheHestonModel? TheHestonModel,namedafterSteveHeston,isatypeofstochasticvolatilitymodelusedbyfinancialprofessionalstopriceEuropeanoptions. more BinomialTree Abinomialtreeisagraphicalrepresentationofpossibleintrinsicvaluesthatanoptionmaytakeatdifferentnodesortimeperiods. more PartnerLinks RelatedArticles AdvancedOptionsTradingConcepts BreakingDowntheBinomialModeltoValueanOption OptionsTradingStrategy&Education TheAnatomyofOptions AdvancedOptionsTradingConcepts UnderstandingtheBinomialOptionPricingModel AdvancedOptionsTradingConcepts CircumventingtheLimitationsofBlack-Scholes RiskManagement WhatIsa"Nonlinear"ExposureinValueatRisk(VaR)? FinancialAnalysis UsingDecisionTreesinFinance