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1、AnImprovedProcedureforVaR/CVaREstimationunderStochasticVolatilityModels1Chuan-HsiangHan2Wei-HanLiu3Tzu-YingChenThisversion:June29,2010Abstract:Thispaperproposesanimprovedprocedureforstochasticvolatilitymodelestimationwithanapplicationinriskmanagement.Thisprocedureiscompos
2、edofthefollowinginstrumentalcomponents:Fouriertransformmethodforvolatilityestimationwithapricecorrectionscheme,andimportancesamplingforextremaleventprobabilityestimationwithapplicationstoestimateValue-at-RiskandconditionalValue-at-Risk.ThenweconductaValue-at-Riskbacktesti
3、ngforsomeforeignexchangedataandtheS&P500indexdata.IncomparisonwithempiricalresultsobtainedfromRiskMetrics,historicalsimulation,andtheGARCH(1,1)model,wefindthatourimprovedprocedureoutperformsonaverage.JELclassification:C13;C14;C63.Keywords:stochasticvolatility,Fouriertrans
4、formmethod,importancesampling,(conditional)Value-at-Risk,backtesting.1DepartmentofQuantitativeFinance,NationalTsing-HuaUniversity,Hsinchu,Taiwan30013,ROC.E-mail:chhan@mx.nthu.edu.tw.WorksupportedbyNSC97-2115-M-007-002-MY2,Taiwan.2SchoolofEconomicsandFinance,LaTrobeUnivers
5、ity,Melbourne,Australia.E-mail:weihanliu2002@yahoo.com.3DepartmentofFinance,NationalTaiwanUniversity.11IntroductionTherearetwomajorapproachesforValue-at-Risk(VaR)andconditionalValue-at-Risk(CVaR)estimation,twoofthemostpopularriskmeasures:modelingthereturndistributionandca
6、pturingthevolatilityprocess(Jorion,2007).Fortheformer,varioustechniquesareemployedformodelingthewholereturndistributionorjustthetailareas,includingknownparametricdistribution,kerneldensityapproximation,andextremevaluetheory,etc.Thelatterheavilyreliesondiscrete-timevolatil
7、itymodelssuchasEWMAandGARCHtocapturethevolatilityprocess.SeeJondeauetal.(2007)forfurtherdetails.Continuous-timestochasticvolatilitymodelsareknownfordemonstratingsomestylizedfeaturesoffinancialdataandtheyhavebeenintensivelyappliedinoptionpricingandhedging.Fouqueetal.(2000)
8、deriveoptionpricingandhedgingapproximationformulaunderthesemodelsbymeansofasingularperturbationt
