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1、TheBlack-ScholesFormulaByGretchenBrowneAbstract:ThemechanicsanduseofEuropeanputandcalloptionsareexplained.Usingthenoarbitrageassumptionasabasisforunderstanding,thederivationoftheBlack-Scholesformulaforoptionpricingisexplained.Therelationshiptotheheatequationofphysicsisshown.Anexampleisgivenofoptionp
2、ricingusingtheformula.Mostofusarefamiliarwithtraditionalinvestmentssuchasstocks,bondsormutualfunds.Relativelyrecently,anewinvestmentclasshasarisen.Thesenewsecuritiesarepricedaccordingtothevalueofanunderlyingasset.Theunderlyingassetmaybeanyofnumberofthings.Somepossibilitiesincludestocks,bonds,interes
3、trates,andcurrencyvaluesamongmanyothers.Sincethevalueofthecontractdependsuponthevalueoftheunderlyingasset,thecontractisconsideredtoderiveitsvaluefromthatasset.Hence,thesecontractsareoftencalled“derivatives.”ThispapershallfocusonaspecifictypeofderivativeknownasaEuropeanputorcalloption,withtheunderlyi
4、ngsecuritybeingastock.Optionsarecontractsgivingtheholder,orpurchaser,ofthecontract“therighttobuyorsellanunderlyingassetatafixedprice.”(Chriss)Whiletheholderhastherighttobuyorselltheunderlyingasset,heorsheisnotobligatedtodoso.Thefixedpriceatwhichtheassetmaybepurchasedorsoldisknownasthestrikepriceorex
5、erciseprice.Therighttobuytheunderlyingsecurityisknownasholdingacalloption.Therighttoselltheunderlyingsecurityfortheexercisepriceiscalledaputoption.Iftheholderoftheoptionchoosestobuyorselltheunderlyingasset,heissaidto“exercisetheoption.”Europeancalloptionsmayonlybeexercisedonasetdate,knownastheexpira
6、tiondate.Thisdatemayalsobesimplytermed“expiry.”Naturally,havingtherighttobuyorselltheunderlyingassetmeanssomeonemustbesellingtherighttobuyorsellthatasset.Thissellerofanoptionissaidto“writeacall.”Inreturnfordoingso,heorshechargesthebuyeraprice.Thispurchasepriceisknownasthepremium.Whilethepurchaser,or
7、holder,oftheoptionhastherighttobuyorsellatthestrikeprice,thewriteroftheoptionisobligatedtosellatthestrikepriceiftheoptionholderchoosestoexercisehisright.CallPutOptionBuyerTherighttobuythestockatthestr
