上财系列 现代金融风险讲义

现代金融风险理论上海财经大学朱文革目录风险的定义风险的分类金融风险理论概述金融风险的非经济学模型金融经济学介绍金融风险的经济学模型风险管理理论概述风险管理实务概述现代金融风险理论第一讲风险的定义HistoricalbackgroundThetermriskmaybetracedbacktoclassicalGreekrizikon(Greekριζα,riza),meaningroot,laterusedinLatinforcliff.ThetermisusedinHomer’sRhapsodyMofOdyssey"Sirens,Scylla,CharybdeeandthebullsofHelios(Sun)"OdysseustriedtosavehimselffromCharybdeeatthecliffsofScylla,wherehisshipwasdestroyedbyheavyseasgeneratedbyZeusasapunishmentforhiscrewkillingbeforethebullsofHelios(thegodofthesun),bygrappingtherootsofawildfigtree.HistoricalbackgroundForsociologists,theterm'risk'isaneologismwhichappearedwiththetransitionfromtraditionaltomodernsociety."IntheMiddleAgesthetermrisciumwasusedinhighlyspecificcontexts,aboveallseatradeanditsensuinglegalproblemsoflossanddamage."Inthevernacularlanguagesofthe16thcenturythewordsrischioandriezgowereused,bothtermsderivedfromtheArabicword"رزق","rizk",meaning'toseekprosperity'.ThiswasintroducedtocontinentalEurope,throughinteractionwithMiddleEasternandNorthAfricanArabtraders.IntheEnglishlanguagethetermriskappearedonlyinthe17thcentury,and"seemstobeimportedfromcontinentalEurope.“Whentheterminologyofrisktookground,itreplacedtheoldernotionthatthought"intermsofgoodandbadfortune."NiklasLuhmann(1996)seekstoexplainthistransition:"Perhaps,thiswassimplyalossofplausibilityoftheoldrhetoricsofFortunaasanallegoricalfigureofreligiouscontentandofprudentiaasa(noble)virtueintheemergingcommercialsociety."风险的教科书定义常见的定义为：uncertaintyconcerningloss。发生财务损失的不确定性，为个人日常生活或企业生命中之常态。是对主观上不确定性的客观衡量。某一事件，在一特定期间后，实际结果与原所预期者，产生偏差的情况。风险的Webster定义ExposuretothechanceofinjuryorlossAhazardordangerouschanceInsurance:ThehazardorchanceoflossThedegreeofprobabilityofsuchlossTheamountthattheinsurancecompanymayloseApersonorthingwithreferencetothehazardinvolvedtotheinsurerThetypeoflossagainstwhichapolicyisdrawn风险三要素风险标的系指暴露在危险情况下之有形的或无形标的危险事故(Peril)源于自然界-天灾(ActsofGod)源于人为因素-人祸(Human’sacts)源于物之本质-物性(Natureofmaterial)危险事故发生的经济结果危险因素实质的危险因素(Physicalhazard)心理的危险因素(Moralehazard)道德的危险因素(Moralhazard)法律危险因素（Legalhazard）风险三要素与风险因素之间的关系危险因素危险事故损失图

1-1危险因素、危险事故与損失之关系图素

因

故

事

险

危損

失

险

危

风险的物理和心理原因测不准原理非线性动力系统博弈论风险的现代汉语词典定义可能发生的危险危险的定义:有遭到损害或失败的可能风险的普通定义Onesetofdefinitionspresentsriskssimplyasfutureissueswhichcanbeavoidedormitigated,ratherthanpresentproblemsthatmustbeimmediatelyaddressed.E.g."Riskistheunwantedsubsetofasetofuncertainoutcomes.“居安思危，思則有备，有备则无患。

－春秋．魏绛《左传》风险的数学期望定义Moreformally(andquantitatively),riskisproportionaltoboththeresultsexpectedfromaneventandtotheprobabilityofthisevent.E.g."Riskisacombinationofthelikelihoodofanoccurrenceofahazardouseventorexposure(s)andtheseverityofinjuryorillhealththatcanbecausedbytheeventorexposure(s)".Mathematically,riskoftensimplydefinedas风险数学期望定义的问题Itis

arguedthatdefiningriskastheproductofimpactandprobabilitypresumes(probablyincorrectly)thatthedecisionmakersareriskneutral.Onlyforariskneutralpersonisthe"certainmonetaryequivalent"exactlyequaltotheprobabilityofthelosstimestheamountoftheloss.Forexample,ariskneutralpersonwouldconsider20%chanceofwinning$1millionexactlyequalto$200,000(ora20%chanceoflosing$1milliontobeexactlyequaltolosing$200,000).However,mostdecisionmakersarenotactuallyriskneutralandwouldnotconsidertheseequivalentchoices.风险的概率定义Itisproposedinsteadthatriskisakindof"vectorquantity"thatdoesnotcollapsetheprobabilityandmagnitudeofariskbypresuminganythingabouttherisktoleranceofthedecisionmaker.Risksaresimplydescribedasansetorfunctionofpossiblelossamountseachassociatedwithspecificprobabilities.Howthisarrayiscollapsedintoasinglevaluecannotbedoneuntiltherisktoleranceofthedecisionmakerisquantified.风险的统计决策定义Instatistics,riskisoftenmappedtotheprobabilityofsomeeventwhichisseenasundesirable.Usually,theprobabilityofthateventandsomeassessmentofitsexpectedharmmustbecombinedintoabelievablescenario(anoutcome),whichcombinesthesetofrisk,regretandrewardprobabilitiesintoanexpectedvalueforthatoutcome.风险的统计决策定义Thus,instatisticaldecisiontheory,theriskfunctionofanestimatorδ(x)foraparameterθ,calculatedfromsomeobservablesx,isdefinedastheexpectationvalueofthelossfunctionL,统计决策三要素样本空间与样本分布族行动空间损失函数选择决策函数的准则容许性准则最小化最大准则贝叶斯准则最优同变性准则风险的经济学定义ExpectedutilityfunctionE[U(X)]whereXisarandomvariable.ConcaveutilityUandriskaversionStochasticDominanceFirstOrderStochasticDominance(FOSD)XFOSDY↔E[u(X)]≥E[u(Y)]forallincreasinguSecondOrderStochasticDominance(SOSD)XSOSDY↔E[u(X)]≥E[u(Y)]forallincreasingandconcaveuButstochasticdominancecannotcomparealldifferentrisks.风险的经济学定义VonNeumann-Morgenstern公理Axiom1:ThepreferenceiscompleteandtransitiveAxiom2:Substitution/IndependenceAxiom3:Continuity/ArchimedeanTheorem:apreferencerelationsatisfiesAxiom1~3iffthereexistsaexpectedutilityfunction风险和不确定性Uncertainty:Thelackofcompletecertainty,thatis,theexistenceofmorethanonepossibility.The"true"outcome/state/result/valueisnotknown.Measurementofuncertainty:Asetofprobabilitiesassignedtoasetofpossibilities.Example:"Thereisa60%chancethismarketwilldoubleinfiveyears"Risk:Astateofuncertaintywheresomeofthepossibilitiesinvolvealoss,catastrophe,orotherundesirableoutcome.Measurementofrisk:Asetofpossibilitieseachwithquantifiedprobabilitiesandquantifiedlosses.Example:"Thereisa40%chancetheproposedoilwellwillbedrywithalossof$12millioninexploratorydrillingcosts".风险和不确定性Inthissense,onemayhaveuncertaintywithoutriskbutnotriskwithoutuncertainty.Wecanbeuncertainaboutthewinnerofacontest,butunlesswehavesomepersonalstakeinit,wehavenorisk.Ifwebetmoneyontheoutcomeofthecontest,thenwehavearisk.Inbothcasestherearemorethanoneoutcome.Themeasureofuncertaintyrefersonlytotheprobabilitiesassignedtooutcomes,whilethemeasureofriskrequiresbothprobabilitiesforoutcomesandlossesquantifiedforoutcomes.现代金融风险理论第二讲风险的分类:Ch1风险的分类纯粹风险及投机风险静态风险与动态风险人身风险、财产风险与责任风险纯粹风险和投机风险依危险事故发生的经济结果，分为：纯粹风险(Purerisk)投机风险(Speculativerisk)：即金融风险保险风险(insurancerisk)风险是損失的不确定性金融风险(financialrisk)风险是損益的不确定性与26风险的分类PureRiskLifeRiskNonlifeRiskFinancialRisk(SpeculativeRisk)SystematicRisk(MarketRisk)CreditRiskLiquidityRiskOperationalRiskLegalRiskPureRiskUncertaintyregardingfrequencyandseverity(processrisk)Uncertaintyregardingmodelstoestimatelosses(parameterrisk)RuinofProbabilityandLossValueLossValueFrequencyRiskRiskManagementPureRisk:NaturalandMan-madeMarketRiskSystematicriskInterestrateriskInflationriskStockmarketriskForeignexchangeriskInflation1960-2002CrudeOilPriceInterestrateriskStockMarketRiskForeignExchangeRiskReturnsonforeignanddomesticinvestmentarenotperfectlycorrelated.FXratesmaynotbecorrelated.Example:$/DMmaybeincreasingwhile$/¥decreasing.UndiversifiedforeignexpansioncreatesFXrisk.CountryorSovereignRiskResultofexposuretoforeigngovernmentwhichmayimposerestrictionsonrepaymentstoforeigners.Lackusualrecourseviacourtsystem.Examples:SouthKorea,Indonesia,Thailand.Morerecently,Argentina.CreditRiskRiskthatpromisedcashflowsarenotpaidinfull.FirmspecificcreditriskSystematiccreditriskTechnologyandOperationalRiskRiskofdirectorindirectlossresultingforminadequateorfailedinternalprocesses,people,andsystemsorfromexternalevents.SomeincludereputationalandstrategicriskTechnologicalinnovationhasseenrapidgrowthAutomatedclearinghousesTechnologyandOperationalRiskRiskthattechnologyinvestmentfailstoproduceanticipatedcostsavings.Riskthattechnologymaybreakdown.LiquidityRiskRiskofbeingforcedtoborrow,orsellassetsinaveryshortperiodoftime.Lowpricesresult.Maygenerateruns.Runsmayturnliquidityproblemintosolvencyproblem.Riskofsystematicbankpanics.LegalRiskNewStatues,courtopinions,regulationLegalriskarisesfromtheactivitiesofaninstitution’smanagement,employeesandagents.现代金融风险理论第三讲风险的非经济学模型:Ch2&3非经济学观点的金融风险模型数学家的观点以死亡风险和灾害风险为例以利率风险为例数学家的观点:拟合风险分布常用的概率分布离散分布连续分布分布函数特征函数MeasureofRiskFrequencyValueSmallLossLargelossExtremeLoss99.9%Confidence肥尾分布正态分布的问题其它分布:尖峰分布t-分布混合分布平稳分布:分形分布Pareto分布尾部的拟合中央部分的拟合随机过程连续过程维纳过程跳跃过程Poisson过程平稳过程宽平稳严平稳平稳的随机过程自相关系数白噪声过程自回归过程移动平均过程ARMAHeavyTailedTimeSeries“ModellingExtremalEvents”byP.Embrechts,CKluppelbergandT.Mikosch,Springer-Verlag世界图书出版社时间序列线性时间序列ARModelsMAModelsARMAModelsARIMAModels非线性时间序列GARCH和ARCHFanandYao《非线性时间序列》科学出版社死亡风险生存函数生存函数的估计生命表的编制长寿风险灾害风险赔款频率赔款额度损失额度的分布信息不完全时怎么办?信度理论巨灾风险利率风险:MeasuresofInterestRateRiskMacaulaydurationrecognizesthatthesensitivityofthepriceofafixedincomeassetisapproximatelyrelatedtothe(presentvalue)weightedaveragetimetomaturityModifieddurationisthenegativeofthefirstderivativeofpricewithrespecttointerestrates,dividedbythepriceModifiedduration=Macaulayduration/(1+r)MacaulayandModifiedDuration

DurationistheSlopeoftheTangencyLineforthePrice/YieldCurvePriceYieldrPrice-yieldcurveforfinancialinstrumentImmunization:anExample

9%10010yr9%Bond29%113.0110yr11%Bond39%69.0430yr6%Bond1YieldPriceMaturityRateImmunizationExample(theXcorporation)TheXCorporationhasanobligationtopay$1millionin10yrs.Itwishestoinvestmoneynowthatwillbesufficienttomeetthisobligation.Xisplanningtoselectfromthethreebondsinthepreviousslide,pleasefindtheimmunizedportfolio.62.144,241.00263,535.74106.231,078.00114,515.94376,889.48---------------1,162.2077.384241.00328,168.58120.391,078.00129,780.42456,386.95----------------1,562.0569.044241.00292,798.64113.011078.00121,824.78414,642.86----------------19.44Bond1PriceSharesValueBond2PriceSharesValueObligationValueSurplus10%8%9%PercentyieldAssumptionsUnderlyingMacaulayandModifiedDurationCashflowsdonotchangewithinterestrates But:thisdoesnotholdfor:CollateralizedMortgageObligations(CMOs)CallablebondsP-Llossreserves–duetoinflation-interestratecorrelationFlatyieldcurve But:generally,yieldcurvesareupward-slopingInterestratesshiftinparallelfashion But:shortterminterestratestendtobemorevolatilethanlongertermratesTherealproblemisthedurationmodelisnotagoodeconomicmodel非经济学金融风险模型的问题优点缺点现代金融风险理论第四讲金融经济学概述风险的经济学观点何为经济学风险的经济学研究方法有何特点WhatisEconomics?TheallocationofscarceresourcesOpportunitycostEfficiencyMicrov.MacroMicro:DecisionsofindividualsandfirmsMarketsforindividualgoodsandservicesMacro:StudyofeconomyasawholeEconomicfluctuations,inflation,etc.EconomictheoryandempiricalanalysisBasicStructureDemand–whatdoconsumersdo?Supply–whatdofirmsdo?Equilibrium–whathappenswhenyouputconsumersandfirmstogether?TheDemandSidePreferences,utilityandbudgetconstraintsIndividualdemandcurvesChoiceovertimeTimepreference&discountingChoiceunderuncertaintyRisk&returnDemandforhedging/insuranceTheSupplySideAllocationofresourcesinproductionAllaboutcostsMarginal,average,sunk,opportunityEconomicversusaccountingprofitsMaximizingpresentvalueSupplycurvesMarketEquilibriumHowequilibriumworksWinners(andlosers?)frommarketequilibriumEfficientmarketsFinancialmarketsGovernmentinterventionWhatisFinance?WhatisFinanceMicro:FinancialEconomicsMacro:MonetaryEconomicsWhatisFinancialEconomics时间和风险的市场均衡TypicalProblemsinFinanceInvestmentFinancingRiskManagementPricing金融经济学:Fisher模型介绍I.Fisher的简单模型模型的假设：消费者（投资者）在‘多’和‘少’之间偏好‘多’消费者（投资者）只考虑现在和将来两期存在理想银行（资本市场），其借贷款利率相同投资机会没有风险Fisher图形将来的消费HFBD现在的消费消费者现有OB，将来有OF。利用银行可以实现不同的选择O将来现在￥25,000￥20,000通过适当借贷，你可以取得HD上的任何一点.HD￥36,000例：假设利率为10%，你现在有￥20，000，将来有￥25，000。如果现在借出￥10，000，将来会有￥25，000+￥10，000*1.1=￥36，000。利率和资产的现值利率是在银行（资本市场上）借（或贷）资本必须支付（或得到）的价格。资产的现值是该资产未来收入在现在的价值。例：年利率为10%，问一年后的110元现在值多少？ 答：PV=挥霍的消费者的选择挥霍的消费者现在借BC，消费OC；将来消费OE将来HFBD现在CE挥霍的消费者的选择O最初的财富节约的消费者的选择节约的消费者现在贷AB，消费OA；将来消费OG将来HFBD现在AG节约的消费者的选择O将来现在￥20,000HD我应该选择哪一点?￥25,000将来现在HD无差异曲线代表消费者效用相同的所有选择￥25,000￥20,000将来现在HD消费者效用增加将来现在L所有的投资机会：现在投资PD，将来得到SPSPOD将来现在LD现在有财富OD，利用投资可以把财富现值增加到OKK*PJM*KT最优策略：利用的投资机会总共为JDO将来现在LDJM*KTFisher模型的几个基本结论技术上的投资机会和所有投资者的主观时间偏好相互作用决定利率。利率决定了资产的价格。在确定的利率下，消费者根据自己的时间偏好确定自己的借贷比例。在确定的利率和投资机会下，企业根据自有资产的多少确定自己的资本结构。资本结构不影响企业的价值如何解决现实世界中的金融问题现实世界和Fisher模型的区别风险投资期利率的期限结构交易成本信息不对称行为理性假设新的模型和金融理论的发展现代金融理论NobelLaureates:Markowitz,Modigliani,Miller,Sharpe,Black&Scholes,Merton现代金融理论利率期限结构理论组合理论和CAPMMM理论动态消费和投资组合理论(MarkowitzTheory->Merton)动态资产定价理论(CAPM->ICAPM)期权和衍生产品理论(Black-Scholes)公司金融理论(MM->Non-PerfectMarket)其它(行为金融学)TheStartingPointforFinanceThestartingpointforeveryfinancialmodelinvolvestheimpectofuncertaintyonthebehaviorofinvestorsand,ultimately,onmarketprices.Indeed,intheabsenceofuncertainty,theproblemsoffinancialeconomicsreducetoexercisesinbasicmicroeconomics.Theveryexistenceoffinancialeconomicsasadisciplineispredictedonuncertainty. Campbell,LoandMackinlay金融风险经济学建模的基本原则现金流原则比较原则无套利原则动态原则风险规避原则现代金融风险理论第五讲金融风险经济学模型:资产组合理论Ch4~9风险和收益收益率的度量风险的度量资产配置收益率的度量-单期持有期收益率(HPR)投资的不确定性和风险投资有风险不同金融工具的不同风险风险的度量收益率的概率分布通过历史数据估计收益率的概率分布投资收益率风险的描述风险描述的特征量：期望值和方差期望值(均值)方差及标准差期望值和方差：例题初期投入：$100期望值=0.3(0.5)+0.5(0.2)+0.2(-0.4)=17%方差=0.3(0.5-0.17)2+0.5(0.2-0.17)+0.2(-0.4-0.17)2=0.0981标准差=(0.0981)0.5=0.313通过历史数据估计投资风险收益率的均值估计样本的平均值收益率的方差估计样本方差资产配置例题假设只有两种资产风险资产:E(rp)=15%p=22%无风险资产:rf

=7%你应该选择怎样的投资组合?资产配置-资本市场线

p=22%

E(rc)=E(rp)*y+rf*(1-y)

c=y*p

F资产配置（续）改变投资组合中风险资产的份额，其组合对应的均值和方差落在一条直线上-theCapitalAllocationLine(CAL)(CAL)的斜率称为Reward-to-VariabilityRatio最优组合的选择和投资者的风险厌恶程度有关风险厌恶的定义：在收益率均值相同的所有投资组合中选择方差最小的。风险厌恶程度的度量风险厌恶程度越大，选择的投资组合相应的点越靠近F经济学中用VonNeuman-Morgenstern效用函数描述风险的厌恶程度效用函数描述风险厌恶SDCAL无风险利率效用增加无差异曲线资产配置例题两种风险资产的组合协方差和相关性何为协方差?度量风险资产收益率变化的相关程度

相关系数在+1和-1之间.

“+1”意味着完全正相关“-1”完全负相关投资组合机会集BAMinimumvariancepoint,Z风险的分散BA=-1=-0.3=1=0当<1时,两个风险资产组合的标准差小于这两个资产标准差的和组合的方差组合中的资产数目系统风险非系统风险随着投资组合中证券数目的增加.组合的风险越来越小不能通过资产组合分散的风险称为系统风险。风险的分散（续）最优投资组合的选择Markowitz理论最优投资组合的选择分3步:找出有效边界利用无风险资产找出CAL根据投资者的风险厌恶程度得到最优组合有效边界xxxxxxxRiskReturn各种不同组合有效边界

MVPZ

有效边界CapitalAllocationLine“M”最优组合“M”CapitalAllocationLine“A”A最优投资组合无风险利率动态资产组合理论R.Merton(1969,1971)Cox&Huang(1989)Karatzas,Lehoczky&Shreve(1986,1987)现代金融风险理论第六讲金融风险经济学模型:CAPM理论资本资产定价模型投资者是市场接受者投资者仅考虑现在和将来投资者可以无限制借贷无交易成本（如税、佣金等）投资者都致力均值-方差最优化所有投资者的信息相同几点结论所有投资者的风险资产投资组合相同市场风险资产组合即投资者的风险资产组合理性投资者的资产组合应为市场风险组合和无风险资产的组合资本市场线M均衡收益率风险-收益匹配是风险的度量，但是否都有价值?风险=系统风险+非系统风险如何估计系统风险?Beta:证券收益率对市场收益率的敏感性度量证券i的特征线=Slope=Interceptri=i+irM+eiBeta和风险

系统风险:非系统风险:

在市场均衡时，所有资产的收益风险比应该相同

资本资产定价模型(CAPM)CAPM:

E(ri):第i种证券的期望收益率

E(rM):市场期望收益率

E(rM)-rf:市场收益升水

rf:无风险利率CAPM-例题假设无风险利率为9%市场收益率为14%第i种证券的Beta为1.3按照CAPM,

证券市场线SMLMA如果证券相应的均值-Beta点不在SML上，其定价错误CAPM的应用证券的成本

资本预算问题证券发行价格的确定CAPM的实证估计案例估计的问题行业BetaPricingformoftheCAPMThepricePofanassetwithpayoffQiswhereisthebetaoftheassetLinearityofPricingCertaintyequivalentpricingformula:ThepricePofanassetwithpayoffQis套利定价模型因素模型套利定价模型因素模型因素的选取方法ExternalfactorsExtractedfactorsFirmcharacteristics套利定价模型APT模型:supposetherearenassetswhoseratesofreturnaregovernedbym<nfactorsaccordingto

thenthereareconstantss.t.现代金融风险理论第七讲金融风险经济学模型:一般投资组合理论ArbitrageTypeAarbitrage:ifaninvestmentproducesanimmediatepositiverewardwithnofuturepayoff(eitherpositiveornegative).TypeBarbitrage:IfaninvestmenthasnonpositivecostbuthasapositiveprobabilityofyieldingapositivepayoffandnoprobabilityofyieldinganegativepayoffPortfolioChoicePortfolioChoicePortfoliochoicetheorem:SupposethatU(x)iscontinuousandincreasetowardsinfinityasxgoestoinfinity. Thentheoptimalportfolioproblemhasasolutionifandonlyifthereisnoarbitragepossibility.PortfoliopricingequationIfisasolutiontotheoptimalportfolioproblem,andthereisarisk-freeinterestrater,thenExample(afilmventure)(Afilmventure)Aninvestorisconsideringthepossibilitiesofinvestinginaventuretoproduceanentertainmentfilm.Hehaslearntthattherearethreepossibleoutcomes,asshowninthenextslide.Healsohastheopportunitytoearn20%riskfreeovertheperiod.Hewantstoknowwhetherheshouldinvestmoneyinthefilmventure;andifso,howmuch?(Pleaseuselogutilityfunction)Example(continue)AnswerExample(Residualrights)Ifitisalsopossibletoinvestinfilmresiduals,whichhavealargepayoffifthefilmishighlysuccessful.Eachdollarinvestedinresidualrightsproduces$6iftheventurehashighsuccessandzerointheothertwocases.Nowwhatshouldtheinvestordo?Example(continue)OptimalPricingUtility-Optimalpricing:ThepricePofanysecurity(orportfolio)withdividenddisIftheutilityfunctionislogfunction,then

whereisthereturnonthelog-optimalportfolio

Example(continue)Supposeanewsecurityisproposedwithpayoffsthatdependsonlyonthepossibleoutcomesofthefilmventure.Ageneralsecurityofthistypewillhavepayoffscorrespondingtohighsuccess,moderatesuccessandfailurerespectively.thereturnonthelog-optimalportfolioisThus,Thelog-optimalpriceofisRisk-NeutralPricing

Example(continue)Usingtherisk-neutralpricing,wehave金融定价基本定理ArbitragefreeStatepricesandcompletemarketEquivalentmartingalemeasure(EMM)Stochasticdiscountfactor(SDF)

金融定价基本定理:（HarrisonandPliska)Supposewehaveamarketofsecurities,thenThemarketisarbitrage-freeifandonlyifthereisatleastoneEMMorSDF;Inwhichcase,themarketiscompleteifandonlyifthereisexactlyonesuchEMMorSDF.PricingAlternativesCAPM和金融定价基本定理的关系APT和金融定价基本定理的关系不同的定价公式Discountedexpectedvalue,CAPMpricing:AnotherformofCAPMutility-optimalpricingRisk-neutralpricing动态资产组合和定价理论动态资产定价理论CCAPM一般均衡模型下的资产定价理论ICAPM动态均衡定价理论现代金融风险理论第八讲金融风险经济学模型:期权定价理论连续时间模型InaMarkovprocessfuturemovementsdependonlyonwhereweare,notthehistoryofhowwegotwhereweareWewillassumethatstockpricesfollowMarkovprocesses弱有效市场Theassertionisthatitisimpossibletoproduceconsistentlysuperiorreturnswithatradingrulebasedonthepasthistoryofstockprices.Inotherwordstechnicalanalysisdoesnotwork.AMarkovprocessforstockpricesisclearlyconsistentwithweak-formmarketefficiencyWiener过程WeconsideravariablezwhosevaluechangescontinuouslyThechangeinasmallintervaloftimeDtisDz

ThevariablefollowsaWienerprocessif:

thevaluesofDzforany2different(non-overlapping)periodsoftimeareindependentMeanof[z(T)–z(0)]is0Varianceof[z(T)–z(0)]isTStandarddeviationof[z(T)–z(0)]is

DifferentiableNotdifferentiableDeterministicStochastic确定函数随机函数Ito过程InanItoprocessthedriftrateandthevarianceratearefunctionsoftimedx=a(x,t)dt+b(x,t)dz

ThediscretetimeequivalentisonlytrueinthelimitasDttendstozeroMonteCarloSimulationWecansamplerandompathsforthestockpricebysamplingvaluesforeSupposem=0.14,s=0.20,andDt=0.01,thenMonteCarloSimulation–OnePath

Ito’s引理Ifweknowthestochasticprocessfollowedbyx,Ito’slemmatellsusthestochasticprocessfollowedbysomefunctionG(x,t)Sinceaderivativesecurityisafunctionofthepriceoftheunderlying&time,Ito’slemmaplaysanimportantpartintheanalysisofderivativesecuritiesTaylorSeriesExpansionATaylor’sseriesexpansionofG(x,t)givesIgnoringTermsofHigherOrderThanDtSubstitutingforDxThee2DtTermTakingLimitsApplicationofIto’sLemma

toaStockPriceProcessExamplesTheConceptsUnderlyingBlack-ScholesTheoptionprice&thestockpricedependonthesameunderlyingsourceofuncertaintyWecanformaportfolioconsistingofthestockandtheoptionwhicheliminatesthissourceofuncertaintyTheportfolioisinstantaneouslyrisklessandmustinstantaneouslyearntherisk-freerateThisleadstotheBlack-ScholesdifferentialequationTheDerivationofthe

Black-ScholesDifferentialEquationTheDerivationofthe

Black-ScholesDifferentialEquationTheDerivationofthe

Black-ScholesDifferentialEquationTheDifferentialEquationAnysecuritywhosepriceisdependentonthestockpricesatisfiesthedifferentialequationTheparticularsecuritybeingvaluedisdeterminedbytheboundaryconditionsofthedifferentialequationInaforwardcontracttheboundaryconditionis ƒ=S–Kwhent=T

Thesolutiontotheequationis ƒ=S–Ke–r(T–t)Risk-NeutralValuationThevariablemdoesnotappearintheBlack-ScholesequationTheequationisindependentofallvariablesaffectedbyriskpreferenceThesolutiontothedifferentialequationisthereforethesameinarisk-freeworldasitisintherealworldThisleadstotheprincipleofrisk-neutralvaluationApplyingRisk-NeutralValuation1.Assumethattheexpectedreturnfromthestockpriceistherisk-freerate2.Calculatetheexpectedpayofffromtheoption3.Discountattherisk-freerateMartingaleMeasure

DriftBrownianMotionBrownianMotion

Where主要结论Thefairpriceistheexpectedvalueofthediscountedfuturestochasticpayoffunderthenewmartingalemeasure.TheBlack-ScholesFormulas

期权风险因素分解期权价格依赖于标的资产价格利率资产收益率的波动性到期时间执行价格现代金融风险理论第九讲金融风险经济学模型:有效市场和行为金融学理论有效市场假设何为有效市场随机行走理论“投镖板”理论随机行走理论股票的价格变动并没有任何固定可测的规律Brown运动随机行走理论续$103.00$100.00$106.09$100.43$97.50$100.43$95.06扔分币游戏HeadsHeadsHeadsTailsTailsTails随机行走理论续随机行走理论续随机行走理论续随机行走理论续随机行走理论续有效市场理论弱有效市场市场价反映了所有历史信息半强有效市场市场价反映了所有公开信息强有效市场市场价反映了所有公开和私人信息预测股票价格的主要检验短期股价的预测几周,几月FilterruleMomentumeffect长期股价预测Reversaleffect股票市场的其它异常现象小企业效应被忽视企业效应P/E效应Book-to-Market比率效应So,AreMarketsEfficient?股票市场的其它现象股票收益率均值和波动性都很高EquitypremiumpuzzleExcessvolatilitypuzzleRisk-freeinterestratepuzzle如何解释MeasurementerrorsSelectionbiasofcountryPesoproblemLimitstoarbitrageUtilityfunctionEpstein-ZinrecursiveutilitypreferencesHabitpersistencepreferences行为金融学HumanPreferencesProspecttheory(Kahneman-Tversky)NarrowframingandmyopiaLossaversionAmbiguityaversionBiasinjudgmentOverconfidenceRepresentativenessConservatismandconfirmationbias反例:AllaisParadoxAllais悖论A={$2500,w.p.10%;$1000,w.p.89%;$0,w.p.1%}B={$1000,w.p.100%}C={$1000,w.p.11%;$0,w.p.89%}D={$2500,w.p.10%;$0,w.p.90%}MajoritychooseB>A,D>C,butthisviolatestheIndependenceAxiom.反例:EllsbergParadox30个红球,60个黑球和黄球,选项1:摸到红球赢100元选项2:摸到黑球赢100元30个红球,60个黑球和黄球,选项1:摸到红球或黄球赢100元选项2:摸到黑球或黄球赢100元前景理论A:50%的概率获得1000元B:肯定获得500元C:50%的概率损失1000元D:肯定损失500元前景理论A:千分之一的概率获得5000元B:肯定获得5元C:千分之一的概率损失5000元D:肯定损失5元框架效应你认为苏联是否应该允许美国新闻记者随意进入其境内采访?你认为美国是否应该允许苏联新闻记者随意进入其境内采访?框架效应你认为美国是否应该允许公开发表反民主的演说?你认为美国是否应该禁止公开发表反民主的演说?框架效应假设甲型H1N1流感可能导致60000人死亡，为了和此斗争，可以有两种备选方案A方案，可以挽救20000人的生命B方案，有1/3的概率挽救60000人，有2/3的概率全部死去框架效应假设甲型H1N1流感可能导致60000人死亡，为了和此斗争，可以有两种备选方案实施C方案，40000人会死亡实施D方案，有1/3的概率没有人死亡，有2/3的概率60000人都会死心理分帐假如你去看电影,门票100元.路上你掉了100元,你还会买票看电影吗?假如你去看电影,已经买了门票,价格100元.路上你掉了电影票,你还会买票看电影吗?心理分帐你准备买一件价值125美元的衣服和一个15美元的计算器。有人告诉你另一家店计算器价格为10美元，但要走20分钟去那家店，你会去吗？你准备买一件价值15美元的衣服和一个125美元的计算器。有人告诉你另一家店计算器价格为120美元，但要走20分钟去那家店，你会去吗？Lossaversion保险公司在原产品的基础上推出新产品,只要缴一半保费。但在事故发生时，如果发生的日子是奇数日，不赔；如果是偶数日，赔。问：你会考虑买这种保险吗？Lossaversion假设甲型H1N1流感可能影响20%的人群，某种疫苗能将被感染的概率降为10%，你会考虑注射这种疫苗吗？假设有两种流感，每种都可能感染10%的人群，某种疫苗能完全防止一种流感，你会考虑注射这种疫苗吗？Lossaversion决斗，共有4颗子弹，你可以出钱去掉一颗子弹，你愿意出多少钱？决斗，共有1颗子弹，你可以出钱去掉这颗子弹，你愿意出多少钱？锚定效应非洲国家的数量在联合国国家总数中所占的百分比是大于65%还是小于65%？你觉得应该是占多少？锚定效应非洲国家的数量在联合国国家总数中所占的百分比是大于10%还是小于10%？你觉得应该是占多少？从众效应大学生救人的故事卖马问题：有人以60美元价格买了一匹马，又以70美元卖出。然后他又以80美元买回这匹马，再以90美元卖出。问他总共赚了多少钱？过度自信天气预报人员和医生的不同问题：一张纸折叠100次后厚度有多少？我最有把握是______厚。我有90%的把握有_____厚。代表性直觉父子俩开车兜风，发生车祸。结果父死子伤。儿子送到医院，需要马上动手术。但外科医生进来后却大吃一惊，说我不能动这个手术，因为他是我儿子。这可能吗？代表性直觉在一个城市所有学生的IQ平均数为100，你任意抽取50人。第一人的IQ为150，问这50人的平均IQ为多少？代表性直觉三个门，其中两个门后面是山羊，一个门后是一箱金币。你选定一个门后，主持人打开剩下的两个门中的一个，放出一只山羊，问你是否要改变你的选择？问你要改变吗？代表性直觉高考成绩和进入大学后的成绩只有中等程度的相关性，大概的情况是高考成绩（百分比）大学成绩>750（前10%）>3.7>700（前20%）>3.5>650（前30%）>3.2>600（前40%）>2.9>500（前50%）>2.5问一个高考成绩725分的人，其大学成绩大概多少？代表性直觉手热现象XOXXXOOOOXOXXOOOXXXOXXOXOXOOOXXOXOXOOXXXOX自我实现三个数的关系符合某个规律，一个例子是2、4、6。希望你找到这个规律。你可以举其它一些例子问我，看是否符合这个规律。问：8、10、12答：符合规律问：12、14、16答：符合规律问：22、24、26答：符合规律问：1、3、5答：符合规律行为陷阱打的例子一美元拍卖的故事拍卖时出价者互相不得交流出价由5美分开始，每次只能加5美分出价不能超过50美元出价最高的前两名都必须付出他们所出的价格，但这一美元只给出价最高的人。深陷泥潭苏联和美国的核竞争认知不协调犹太人的故事足球场的故事接待中国人的问卷现代金融风险理论第十讲同学讨论和演讲:风险部分现代金融风险理论第十一讲金融