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1、MCMCMethodsforFinancialEconometricsMichaelJohannesandNicholasPolson∗May8,2002AbstractThischapterdiscussesMarkovChainMonteCarlo(MCMC)basedmethodsfores-timatingcontinuous-timeassetpricingmodels.WedescribetheBayesianapproachtoempiricalassetpricing,themechanicsofMCMCalgorithmsandthestrongthe
2、oreticalunderpinningsofMCMCalgorithms.WeprovideatutorialonbuildingMCMCalgo-rithmsandshowhowtoestimateequitypricemodelswithfactorssuchasstochasticexpectedreturns,stochasticvolatilityandjumps,multi-factortermstructuremodelswithstochasticvolatility,time-varyingcentraltendancyorjumpsandregim
3、eswitchingmodels.∗WethanktheEditors,YacineAit-SahaliaandLarsHansenandChrisSimsforhisdiscussion.WealsothankMarkBroadie,MikeChernov,AnneGronandPaulGlassermanfortheirhelpfulcomments.JohannesisattheGraduateSchoolofBusiness,ColumbiaUniversity,3022Broadway,NY,NY,10027,mj335@columbia.edu.Polson
4、isattheGraduateSchoolofBusiness,UniversityofChicago,1101East58thStreet,ChicagoIL60637,ngp@gsbngp.uchicago.edu.1Contents1Introduction32OverviewofMCMC63BayesianInferenceandAssetPricingModels93.1PricesandtheLikelihoodFunction........................103.2StateVariableDynamics................
5、..............123.3ParameterDistribution...............................133.4Time-Discretization.................................154AssetPricingModels184.1Continuous-timeEquityPriceModels.......................184.2AffineDiffusionTermstructuremodels......................194.3Continuous-timeM
6、arkovSwitchingModels....................204.4Equityindexoptionpricingmodels........................214.5StructuralModelsofDefault............................215MCMCmethods:Theory225.1Hammersley-CliffordTheorem...........................225.2GibbsSampling...................................
7、235.3Metropolis-Hastings.................................255.3.1IndependenceMetropolis-Hastings.....................265.3.2Random-WalkMetropolis.........................275.4ConvergenceTheory................................275.4.1ConvergenceofMarkovChains.................
