An Elementary Introduction to Mathematical Finance资料下载.pdf

An Elementary Introduction to Mathematical Finance资料下载.pdf

《An Elementary Introduction to Mathematical Finance资料下载.pdf》由会员分享，可在线阅读，更多相关《An Elementary Introduction to Mathematical Finance资料下载.pdf（323页珍藏版）》请在冰点文库上搜索。

ThispageintentionallyleftblankAnElementaryIntroductiontoMathematicalFinance,ThirdEditionThistextbookonthebasicsofoptionpricingisaccessibletoreaderswithlimitedmathematicaltraining.Itisforbothprofessionaltradersandun-dergraduatesstudyingthebasicsoffinance.Assumingnopriorknowledgeofprobability,SheldonM.Rossoffersclear,simpleexplanationsofarbi-trage,theBlackScholesoptionpricingformula,andothertopicssuchasutilityfunctions,optimalportfolioselections,andthecapitalassetspricingmodel.Amongthemanynewfeaturesofthisthirdeditionarenewchap-tersonBrownianmotionandgeometricBrownianmotion,stochasticorderrelations,andstochasticdynamicprogramming,alongwithexpandedsetsofexercisesandreferencesforallthechapters.SheldonM.RossistheEpsteinChairProfessorintheDepartmentofIndustrialandSystemsEngineering,UniversityofSouthernCalifornia.HereceivedhisPh.D.instatisticsfromStanfordUniversityin1968andwasaProfessorattheUniversityofCalifornia,Berkeley,from1976until2004.Hehaspublishedmorethan100articlesandavarietyoftextbooksintheareasofstatisticsandappliedprobability,includingTopicsinFiniteandDiscreteMathematics（2000）,IntroductiontoProbabilityandStatis-ticsforEngineersandScientists,FourthEdition（2009）,AFirstCourseinProbability,EighthEdition（2009）,andIntroductiontoProbabilityModels,TenthEdition（2009）.Dr.RossservesastheeditorforProbabil-ityintheEngineeringandInformationalSciences.AnElementaryIntroductiontoMathematicalFinanceThirdEditionSHELDONM.ROSSUniversityofSouthernCaliforniaCAMBRIDGEUNIVERSITYPRESSCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SoPaulo,Delhi,Tokyo,MexicoCityCambridgeUniversityPress32AvenueoftheAmericas,NewYork,NY10013-2473,USAwww.cambridge.orgInformationonthistitle:

@#@www.cambridge.org/9780521192538CambridgeUniversityPress1999,2003,2011Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionsofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublished1999Secondeditionpublished2003Thirdeditionpublished2011PrintedintheUnitedStatesofAmericaAcatalogrecordforthispublicationisavailablefromtheBritishLibrary.LibraryofCongressCataloginginPublicationdataRoss,SheldonM.（SheldonMark）,1943Anelementaryintroductiontomathematicalfinance/SheldonM.Ross.Thirdedition.p.cm.Includesindex.ISBN978-0-521-19253-81.InvestmentsMathematics.2.Stochasticanalysis.3.Options（Finance）Mathematicalmodels.4.SecuritiesPricesMathematicalmodels.I.Title.HG4515.3.R672011332.601?

@#@51dc222010049863ISBN978-0-521-19253-8HardbackCambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofURLsforexternalorthird-partyinternetwebsitesreferredtointhispublicationanddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.Tomyparents,EthelandLouisRossContentsIntroductionandPrefacepagexi1Probability11.1ProbabilitiesandEvents11.2ConditionalProbability51.3RandomVariablesandExpectedValues91.4CovarianceandCorrelation141.5ConditionalExpectation161.6Exercises172NormalRandomVariables222.1ContinuousRandomVariables222.2NormalRandomVariables222.3PropertiesofNormalRandomVariables262.4TheCentralLimitTheorem292.5Exercises313BrownianMotionandGeometricBrownianMotion343.1BrownianMotion343.2BrownianMotionasaLimitofSimplerModels353.3GeometricBrownianMotion383.3.1GeometricBrownianMotionasaLimitofSimplerModels403.4TheMaximumVariable403.5TheCameron-MartinTheorem453.6Exercises464InterestRatesandPresentValueAnalysis484.1InterestRates484.2PresentValueAnalysis524.3RateofReturn624.4ContinuouslyVaryingInterestRates654.5Exercises67viiiContents5PricingContractsviaArbitrage735.1AnExampleinOptionsPricing735.2OtherExamplesofPricingviaArbitrage775.3Exercises866TheArbitrageTheorem926.1TheArbitrageTheorem926.2TheMultiperiodBinomialModel966.3ProofoftheArbitrageTheorem986.4Exercises1027TheBlackScholesFormula1067.1Introduction1067.2TheBlackScholesFormula1067.3PropertiesoftheBlackScholesOptionCost1107.4TheDeltaHedgingArbitrageStrategy1137.5SomeDerivations1187.5.1TheBlackScholesFormula1197.5.2ThePartialDerivatives1217.6EuropeanPutOptions1267.7Exercises1278AdditionalResultsonOptions1318.1Introduction1318.2CallOptionsonDividend-PayingSecurities1318.2.1TheDividendforEachShareoftheSecurityIsPaidContinuouslyinTimeataRateEqualtoaFixedFractionfofthePriceoftheSecurity1328.2.2ForEachShareOwned,aSinglePaymentoffS（td）IsMadeatTimetd1338.2.3ForEachShareOwned,aFixedAmountDIstoBePaidatTimetd1348.3PricingAmericanPutOptions1368.4AddingJumpstoGeometricBrownianMotion1428.4.1WhentheJumpDistributionIsLognormal1448.4.2WhentheJumpDistributionIsGeneral1468.5EstimatingtheVolatilityParameter1488.5.1EstimatingaPopulationMeanandVariance1498.5.2TheStandardEstimatorofVolatility150Contentsix8.5.3UsingOpeningandClosingData1528.5.4UsingOpening,Closing,andHighLowData1538.6SomeComments1558.6.1WhentheOptionCostDiffersfromtheBlackScholesFormula1558.6.2WhentheInterestRateChanges1568.6.3FinalComments1568.7Appendix1588.8Exercises1599ValuingbyExpectedUtility1659.1LimitationsofArbitragePricing1659.2ValuingInvestmentsbyExpectedUtility1669.3ThePortfolioSelectionProblem1749.3.1EstimatingCovariances1849.4ValueatRiskandConditionalValueatRisk1849.5TheCapitalAssetsPricingModel1879.6RatesofReturn:

@#@Single-PeriodandGeometricBrownianMotion1889.7Exercises19010StochasticOrderRelations19310.1First-OrderStochasticDominance19310.2UsingCouplingtoShowStochasticDominance19610.3LikelihoodRatioOrdering19810.4ASingle-PeriodInvestmentProblem19910.5Second-OrderDominance20310.5.1NormalRandomVariables20410.5.2MoreonSecond-OrderDominance20710.6Exercises21011OptimizationModels21211.1Introduction21211.2ADeterministicOptimizationModel21211.2.1AGeneralSolutionTechniqueBasedonDynamicProgramming21311.2.2ASolutionTechniqueforConcaveReturnFunctions21511.2.3TheKnapsackProblem21911.3ProbabilisticOptimizationProblems221xContents11.3.1AGamblingModelwithUnknownWinProbabilities22111.3.2AnInvestmentAllocationModel22211.4Exercises22512StochasticDynamicProgramming22812.1TheStochasticDynamicProgrammingProblem22812.2InfiniteTimeModels23412.3OptimalStoppingProblems23912.4Exercises24413ExoticOptions24713.1Introduction24713.2BarrierOptions24713.3AsianandLookbackOptions24813.4MonteCarloSimulation24913.5PricingExoticOptionsbySimulation25013.6MoreEfficientSimulationEstimators25213.6.1ControlandAntitheticVariablesintheSimulationofAsianandLookbackOptionValuations25313.6.2CombiningConditionalExpectationandImportanceSamplingintheSimulationofBarrierOptionValuations25713.7OptionswithNonlinearPayoffs25813.8PricingApproximationsviaMultiperiodBinomialModels25913.9ContinuousTimeApproximationsofBarrierandLookbackOptions26113.10Exercises26214BeyondGeometricBrownianMotionModels26514.1Introduction26514.2CrudeOilData26614.3ModelsfortheCrudeOilData27214.4FinalComments27415AutoregressiveModelsandMeanReversion28515.1TheAutoregressiveModel28515.2ValuingOptionsbyTheirExpectedReturn28615.3MeanReversion28915.4Exercises291Index303IntroductionandPrefaceAnoptiongivesonetheright,butnottheobligation,tobuyorsellasecurityunderspecifiedterms.Acalloptionisonethatgivestherighttobuy,andaputoptionisonethatgivestherighttosellthesecurity.Bothtypesofoptionswillhaveanexercisepriceandanexercisetime.Inaddition,therearetwostandardconditionsunderwhichoptionsoper-ate:

@#@Europeanoptionscanbeutilizedonlyattheexercisetime,whereasAmericanoptionscanbeutilizedatanytimeuptoexercisetime.Thus,forinstance,aEuropeancalloptionwithexercisepriceKandexercisetimetgivesitsholdertherighttopurchaseattimetoneshareoftheunderlyingsecurityforthepriceK,whereasanAmericancalloptiongivesitsholdertherighttomakethepurchaseatanytimebeforeorattimet.Aprerequisiteforastrongmarketinoptionsisacomputationallyeffi-cientwayofevaluating,atleastapproximately,theirworth;@#@thiswasaccomplishedforcalloptions（ofeitherAmericanorEuropeantype）bythefamousBlackScholesformula.TheformulaassumesthatpricesoftheunderlyingsecurityfollowageometricBrownianmotion.ThismeansthatifS（y）isthepriceofthesecurityattimeythen,foranypricehistoryuptotimey,theratioofthepriceataspecifiedfuturetimet+ytothepriceattimeyhasalognormaldistributionwithmeanandvarianceparameterstandt2,respectively.Thatis,log?

@#@S（t+y）S（y）?

@#@willbeanormalrandomvariablewithmeantandvariancet2.BlackandScholesshowed,undertheassumptionthatthepricesfollowageo-metricBrownianmotion,thatthereisasinglepriceforacalloptionthatdoesnotallowanidealizedtraderonewhocaninstantaneouslymaketradeswithoutanytransactioncoststofollowastrategythatwillre-sultinasureprofitinallcases.Thatis,therewillbenocertainprofit（i.e.,noarbitrage）ifandonlyifthepriceoftheoptionisasgivenbytheBlackScholesformula.Inaddition,thispricedependsonlyonthexiiIntroductionandPrefacevarianceparameterofthegeometricBrownianmotion（aswellasontheprevailinginterestrate,theunderlyingpriceofthesecurity,andtheconditionsoftheoption）andnotontheparameter.Becausethepa-rameterisameasureofthevolatilityofthesecurity,itisoftencalledthevolatilityparameter.Arisk-neutralinvestor