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1、ComputingtheCEVoptionpricingformulausingthesemiclassicalapproximationofpathintegralAxelA.Araneda∗andMarceloJ.Villena†‡Lastversion:March29,2018AbstractTheConstantElasticityofVariance(CEV)modelsignificantlyoutperformstheBlack-Scholes(BS)modelinforecastingbothpricesandoptions.Furtherm
2、ore,theCEVmodelhasamarkedadvantageincapturingbasicempiricalregularitiessuchas:heteroscedasticity,theleverageeffect,andthevolatilitysmile.Infact,theperformanceoftheCEVmodeliscomparabletomoststochasticvolatilitymodels,butitisconsiderableeasiertoimplementandcalibrate.Nevertheless,thes
3、tandardCEVmodelsolution,usingthenon-centralchi-squareapproach,stillpresentshighcomputationaltimes,speciallywhen:i)thematurityissmall,ii)thevolatilityislow,oriii)theelasticityofthevariancetendstozero.Inthispaper,anewnumericalmethodforcomputingtheCEVmodelisdeveloped.Thisnewapproachi
4、sbasedonthesemiclassicalapproximationofFeynman’spathintegral.OursimulationsshowthatthemethodisefficientandaccuratecomparedtothestandardCEVsolutionconsideringthepricingofEuropeancalloptions.Keywords:Optionpricing,constantelasticityofvariancemodel,pathintegral,numericalmethods.arXiv:1
5、803.10376v1[q-fin.CP]28Mar2018∗FacultyofEngineering&Sciences,UniversidadAdolfoIbáñez,Avda.DiagonallasTorres2640,Peñalolén,7941169Santiago,Chile.Email:axel.araneda@edu.uai.cl.†UniversidadAdolfoIbáñez,Address:DiagonalLasTorres2640,Peñalolén,Santiago,Chile.Telephone:56-223311491,Emai
6、l:marcelo.villena@uai.cl.‡AidfromtheFondecytProgram,projectNº1131096,isgratefulacknowledgedbyMarcelo.11IntroductionOneofthemostsignificantlimitationsoftheBlack-Scholes(BS)[1]modelistheassumptionofconstantvolatility,whichignoressomewell-knownempiricalregularitiessuchas:theleverageeff
7、ect[2,3],andthevolatilitysmile[4,5].Theseshortcomingshaveinspiredseveralnon-constantvolatilitymodelsincontinuoustime1,considering‘stochasticvolatility’2or‘level-dependentvolatility’models3[10].Intheformer,boththeassetandthevolatilityhavetheirowndiffusionprocesses.Inthelevel-depende
8、ntvolatilitymodelsonlytheassetisg
