book2-Market Risk Measurement and Management_wrapper.pdfVIP免费

````AnexampleofanHSVaRisgiveninFigure1.2.Thisfigureshowsthehistogramof1000hypotheticallossobserva­tionsandthe95%VaR.Thefigureisgeneratedusingthe,hsvarfigure'commandintheMMRToolbox.TheVaRis1.704andseparatesthetop5%fromthebottom95%oflossobservations.706050。4huanbaJ::t302010，．'，'，，俨�r一95%VaR=1.704俨F尸尸尸...>-���尸>-...���俨...卜一�卜一...,俨�听.....n，0_4-3-2-101Loss(+)/profit(一）IFigure1.21k>uanbaJ:I10.90.80.70.60.50.40.30.20.10_4HistoricalsimulationVaR.-3IFigure1.3J-2cumulativefrequencyfunction.Note:BasedonthesamedataasFigure1.2.2Note:Basedon1000randomnumbersdrawnfromastandardnormalUPdistribution,andestimatedwith'hsvarfigure'function.2395%VaR=1.704-101Loss(+)/profit(一）Historicalsimulationviaanempirical3Inpractice,itisoftenhelpfultoobtainHSVaRestimatesfromacumulativehistogram,orempiricalcumulativefrequencyfunction.Thisisaplotoftheorderedlossobservationsagainsttheirempiricalcumulativefrequency(e.g.,soiftherearenobservationsintotal,theempiricalcumulativefrequencyoftheithsuchorderedobservationisi/n).Theempiricalcumu­lativefrequencyfunctionofourearlierdatasetisshowninFigure1.3.TheempiricalfrequencyfunctionmakesitveryeasytoobtaintheVaR:wesimplymoveupthecumulativefrequencyaxistowherethecumulativefrequencyequalsourconfidencelevel,drawahorizontallinealongtothecurve,andthendrawaverticallinedowntothex-axis,whichgivesusourVaR.1.3ESTIMATINGPARAMETRICVAR4WecanalsoestimateVaRusingparametricapproaches,thedistinguishingfeatureofwhichisthattheyrequireustoexplicitlyspecifythestatisticaldistributionfromwhichourdataobservationsaredrawn.WecanalsothinkofparametricapproachesasfittingcurvesthroughthedataandthenreadingofftheVaRfromthefittedcurve.Inmakinguseofaparametricapproach,wethereforeneedtotakeaccountofboththestatisticaldistributionandthetypeofdatatowhichitapplies.EstimatingVaRwithNormallyDistributedProfits/LossesSupposethatwewishtoestimateVaRundertheassumptionthatP/Lisnormallydistributed.InthiscaseourVaRattheconfi­dencelevelais:aVaR=-µ,盯L+�盯LZaaVa�=-mP/L...