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1、Chapter5:OptionPricingModels: TheBlack-ScholesModelWhenIfirstsawtheformulaIknewenoughaboutittoknowthatthisistheanswer.Thissolvedtheancientproblemofriskandreturninthestockmarket.Itwasrecognizedbytheprofessionforwhatitwasasarealtourdeforce.MertonMillerTrillionDollarBet
2、,PBS,February,2000D.M.ChanceCh.5:1AnIntroductiontoDerivativesandRiskManagement,6thed.ImportantConceptsinChapter5TheBlack-ScholesoptionpricingmodelTherelationshipofthemodel’sinputstotheoptionpriceHowtoadjustthemodeltoaccommodatedividendsandputoptionsTheconceptsofhisto
3、ricalandimpliedvolatilityHedginganoptionpositionD.M.Chance2AnIntroductiontoDerivativesandRiskManagement,6thed.OriginsoftheBlack-ScholesFormulaBrownianmotionandtheworksofEinstein,Bachelier,Wiener,ItôBlack,Scholes,Mertonandthe1997NobelPrizeD.M.Chance3AnIntroductiontoDe
4、rivativesandRiskManagement,6thed.TheBlack-ScholesModelastheLimitoftheBinomialModelRecallthebinomialmodelandthenotionofadynamicrisk-freehedgeinwhichnoarbitrageopportunitiesareavailable.ConsidertheAOLJune125calloption.Figure5.1,p.131showsthemodelpriceforanincreasingnum
5、beroftimesteps.Thebinomialmodelisindiscretetime.Asyoudecreasethelengthofeachtimestep,itconvergestocontinuoustime.D.M.Chance4AnIntroductiontoDerivativesandRiskManagement,6thed.TheAssumptionsoftheModelStockPricesBehaveRandomlyandEvolveAccordingtoaLognormalDistribution.
6、SeeFigure5.2a,p.134,5.2b,p.135and5.3,p.136foralookatthenotionofrandomness.Alognormaldistributionmeansthatthelog(continuouslycompounded)returnisnormallydistributed.SeeFigure5.4,p.137.TheRisk-FreeRateandVolatilityoftheLogReturnontheStockareConstantThroughouttheOption’s
7、LifeThereAreNoTaxesorTransactionCostsTheStockPaysNoDividendsTheOptionsareEuropeanD.M.Chance5AnIntroductiontoDerivativesandRiskManagement,6thed.ANobelFormulaTheBlack-ScholesmodelgivesthecorrectformulaforaEuropeancallundertheseassumptions.Themodelisderivedwithcomplexma
8、thematicsbutiseasilyunderstandable.TheformulaisD.M.Chance6AnIntroductiontoDerivativesandRiskManagement,6thed.ANobelFormula(continue
