金融风险度量方法简介及VaR和ES与会计变量的关系

华中科技大学硕士学位论文金融风险度量方法简介及VaR和ES与会计变量的关系姓名：田立申请学位级别：硕士专业：概率论与数理统计指导教师：刘小茂20060418I1.VaRESVaRES2.200213VaRESVaRESVaRESVaRES3.VaRES200112002121519VaRESVaRESVaRESIIAbstractInthebackgroundofthefinancialglobalization,financialrisksmanagementisahottopicforrecentyears.So,howtomeasurethesefinancialrisksisaproblemneedtobesolvedfirstlyandurgently.Inthispaper,wediscusseachchiefriskmeasurementssystemically.Theirpropertiesandcomputationarithmeticaregeneralizedtheireconomicimplicationsareintroduceddetailed.Thenthecomparisonbetweenthemontheiradvantagesanddisadvantagesarediscussedandsomeinterestingresultsareobtained.Theseriskmeasurementssettheirbasesonstatisticsandmathematicalalgorithms,combinedwithmarketablemovement.Themainworksofthispaperareasfollows:1.Therearesomeintroductionsonmodernriskmeasurement.Eachriskmeasurements’definitions,properties,calculationandappraisementarithmeticareintroduced;especiallysomeinnovationsaremadeonESandspectralriskmeasurement’spropertiesandcalculation.2.Therearecomparisonsandanalysesonmodernmainlyriskmeasurements.13stocksareselectedfromShenzhenstockmarketin2002byclusteringanalyzingmethod,andcalculateVaRandESbyhistoricalsimulation.WevalidatesomeoftheirspropertiesandtherelationbetweenVaRandES.Furthermore,WevalidatethecoherenceofthesolutionstotheefficientportfoliobasedonVariance,VaRandESseparatelyundertheassumptionofthenormaldistribution.3.AdvancesomehypothesesontherelationsnotonlybetweenfiscalvariablesandVaRbutalsobetweenfiscalvariablesandES.Weselect151stocks’datuminShanghaistockmarketfromJan.2001toDec.2002,calculateVaRandESbyweightedhistoricalsimulation.9fiscalvariablesthatreflectthecorporation’scharacteristicareselectedand7hypothesesareadvancedbasedonthefiscaltheories.CovariancebetweenVaRandfiscalvariablesandbetweenESandfiscalvariablesandlinearregressionsaboutVaRandlinearregressionsaboutESon9fiscalvariablesarecalculatedtoverifythehypotheses.Atlast,wementionedthedirectionsofthefurtherresearch.Keywords:Riskmeasurements,VaR,ES,Spectralmeasuresofrisk,Coherentmeasureofrisk,Fiscalvariables,Remarkablycorrelative111.1Knight19212creditriskliquidityrisk(interestraterisk)(foreignexchangerisk)(operationrisk)(legalrisk)(inflationrisk)(circumstancerisk)(policyrisk)(countryrisk)1020(Black-Scholes)(),70,70,[1]207020803,,()(),1.219521990Markowitz[2-3](Sharpe,WillamF)(Linter,John)19641965[4-5]CapitalassetpricingmodelCAPM204VaRVaRValueatRisk20601994J.P.MorganVaR30140VaRVaRBLSEUInternationalSwapsandDerivativesAssociationVaR1998VaRVaRVaR[68]VaRVaRVaRMVaRVaRCVaRVaRIVaR[9-13]VaRVaRVaRVaRVaRVaRArtzner1999[27]VaR2002RockafellarUryasevCVaRConditionalValueatRisk[29]Acerbi,C.5TascheESExpectedShortfall[30-31]CVaRESCVaRESCVaRCVaRtCVaRCVaR[34-36]AcerbiC.,NordioC.SirtoriCTCETailConditionalExpectationWCEWorstConditionalExpectation[30]ESES2002AcerbiESSpectralRiskMeasureVaRESMonteCarlodeltadeltaGARCHgammagammaGARCH[14-21]VaRESVaRESββ[39-47]1.36VaRES7VaRESVaRES72X2.12.1.1X2[]XEXEXσ=−E1952Markowitz[1-2]2.1.21.2.3.82.2VaR2.2.1VaRVaRPhilippeJorion[6]()inf{,()}VaRXxRPXxαα=∈≤−≥α0.1Xt∆X()1PXVaRαα−=−2.2.2VaRΩVaR[15](1):,cRX∀∈∀∈Ω()()VaRXcVaRXcαα+=−(2)0,cRX∀≥∈∀∈Ω()()VaRcXcVaRXαα=(3),XY∀∈Ω,XYϕ[()][()]EXEYϕϕ≤()()VaRXVaRY≥XY≤()()VaRXVaRY≥(4),XY∀∈Ωc∀∈()()PXcPYc≤=≤()()VaRXVaRYαα=(5)XY()()()VaRXYVaRXVaRYααα+=+9145f()XfU=(()())PfUfα≤()PUαα=≤=()()VaRXfαα=−g()()VaRYgαα=−gf+{((()()))}PXYfgαα+≤−−+{()()}PXYfgαα=+≤+{()()()()}PfUgUfgαα+≤+()PUα=≤α=()()()VaRXYVaRXVaRYααα+=+(6)1()=()VaRXVaRXαα−−−2.2.3VaRVaRMonteCarlo(1)[16]VaR(2)10adelta[17](,)PtW(,)PtWtW(,)/t,(,)/tPPtWgPtWW=∂∂=∂∂0T0000(,)=(,)+()+g()tPtWPtWPttWW−−W(0,)rNV∼00(,)(,)PPtWPtW∆=−(,)TtNPtgVg∆()TtVaRPtzgVgαα=−∆−()zααbdeltaGARCH[18]{}tXHsiehEGARCH{}tX2211231412lnln[||]tttttttXzaaazazσσµσπ−−−=+=++−+tz(t-1)011a234,,aaa34,aa02tσ1tη−340,0aa=12||tηπ−2tσ340,0aa=10tη−2tσ[19]tztGEDEGARCHt()tVaRzαµασ=−−deltatgamma[20]gammaGARCH[21]11VaR[12]VaR3MonteCarloMonteCarlo[22]VaRMonteCarloJamshudianZhuscenario[23]MarkovChainMonteCarlo(MCMC)[24]4[25]1...nXXn(1)1{}miniinXX≤≤=kn{},{}nnαβn→∞*(1)(1)()nnXXβα−=*()Fx1.k=0,Gumbel*()1exp(exp())Fxx=−−x∈2.k0,Frechet1*1exp((1)()0kkxFx−−+=1xkelse−3.k0,Weibull1*1exp((1)()0kkxFx−−+=1xkelse−Tasy,R.S.(1)(1)[ln]{1[ln]}lnknnnnnnnnkVaRααααββα−−−−−−=+00nnkk=≠12,,nnnkαβnnCoxandHinkley(1974,p.467)HillPickands1975[26]VaR2.2.4VaRVaR[6,14]VaR[15,27,28]VaR,VaR,,VaRVaR,,,VaRVaR,VaRVaRVaRVaRVaR2.3CVaRES2.3.1VaRArtzner1999[27]ρΩ13:RρΩ→1,cRX∀∈∀∈Ω()()XcXcρρ+=−20,cRX∀≥∈∀∈Ω()()cXcXρρ=3,,XYXY∀+∈Ω()()()XYXYρρρ+≤+4,,XYYX∀∈Ω≤()()XYρρ≤ρ2.3.1()VaRXα1(())PXVaRXαα≤−=(())PYVaRYαα≤−=YX≥(())PXVaRYαα≤−≤()()VaRYVaRXαα≤()VaRXα142()VaRXα(())PXVaRXαα≤−=())PXcVaRXcαα⇔+≤−+=((())PXcVaRXcαα+≤−−=()()VaRXcVaRXcαα⇔+=−()VaRXα3c(())PXVaRXαα≤−=((()))PcXcVaRXαα⇔≤−⋅=()()VaRcXcVaRXαα=⋅()VaRXα4()VaRXα2.3.12.3.1()XY(,1)−∞(,)XY(,)PXXYy1(2)(2)xy=−−,1xy222(3)()4(4)LogxPXYxxx−+≤=+−−2x151()21VaRXαα=−−1()21VaRYαα=−−2()44VaRXYαα+≥−−()()()VaRXYVaRXVaRYααα+≥+0.99α=0.99()98VaRX=0.99()98VaRY=0.99()2032VaRXY+=()VaRXα()VaRXα2.3.1VaRVaRCVaRConditionalValuevatRiskESExpectShortfall2.3.2CVaRESRockafellarUryasevCVaR