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1、Chapter6ExactandAlmostExactSimulationTheaimofthischapteristodiscussthesimulationoftractablemodels,illustratedinthecontextofstochasticvolatilitymodels.Fortwopopularstochasticvolatilitymodels,theHestonmodel,seeHeston(1993),andthe3/2model,seeHeston(1997)andLewis(2000),wepresentexactsimulat
2、ionalgorithms,whereweuseresultsfromSect.5.4.Thesetechniquesarebasedontheinversetransformmethod,whichweÞrstlyrecall.Movingtohigherdimensions,itseemsmoredifÞculttogeneralizethesetechniquesexceptforthetrivialdependencestructure,theindependentcase.Consequently,werecallalmostexactsimulations
3、chemesfromPlatenandBruti-Liberati(2010),whichareapplicableinthemultidimensionalcase.Finally,wepointoutthatinChap.11wewilldiscussadvancedmultidimensionalstochasticvolatilitymodelsbasedontheWishartprocess,whichhavebeensuccessfullyappliedtothemodelingofstochasticvolatility.Weintroducethese
4、simulationmethodsinanequitycontext,inparticular,weconcentrateonmodelingstocksandstockindices.However,thesemethodsarealsoapplicableinotherareas,forexampleininterestratemodeling:thestochasticvolatilityBrace-Ga¸tarek-MusielamodelintroducesstochasticvolatilityprocessesinthecontextoftheLIBOR
5、marketmodel.Thetechniquesdiscussedinthischapterarealsoapplicableinsuchacontext,seee.g.Chap.16inBrace(2008),inparticular,Sect.16.4,whichdealswithsimulation.6.1SamplingbyInverseTransformMethodsConceptually,wesimulatethegivenmodels,one-andmultidimensionalmodels,us-ingtheinversetransformmet
6、hod,whichwasdiscussede.g.inChap.2inPlatenandBruti-Liberati(2010).Theforthcomingbriefdescriptionoftheinversetransformmethodfollowsthisdiscussionclosely.Thewell-knowninversetransformmethodcanbeappliedforthegenerationofacontinuousrandomvariableYwithgivenprobabilitydistributionfunctionFY.Fr
7、omJ.Baldeaux,E.Platen,FunctionalsofMultidimensionalDiffusionswithApplications161toFinance,Bocconi&SpringerSeries5,DOI10.1007/978-3-319-00747-2_6,©SpringerInternationalPublishingSwitzerland20131626ExactandAlmostExactSimulationauniformlydistributedrandomvariable0
