投资组合动态VaR风险度量_许启发

236Vol.23　No.6Statistics&InformationForum20086Jun.,2008:2008-02-18;:2008-04-30:《Copula》(70671074);《、》(20060400192);《》(2006B07);《》(07JC790046)、《》(06JD910006):(1975-),,,,,:。【】投资组合动态VaR风险度量许启发1,2(1.,　300072;2.,　364005):VaR,,VaR。ICA,ICAVaR,VaR。,EWMA、MGARCH,ICAVaR。:VaR;;;:F830　　:A　　:1007-3116(2008)06-0040-07一、引　言VaR(valueatrisk)Bau-mol(1963):1993,、G-30,VaR、。1994,J.P.MorganVaRRiskMetrics,14300,。VaR,。VaR,VaR,VaR。,VaR。VaR,VaR:、MonteCarlo。,,VaR,VaR,,“”。,VaR,、t,,;tt,。,VaR。(indepen-dentcomponentanalysis,ICA),;40GARCD-JSU;MonteCarloVaR。,:,(exponentiallyweightedmovingaverage,EWMA)、GARCH(multivariateGARCH,MGARCH)ICAVaR,。二、单个资产VaR风险度量()VaRVaR、,,VaRα(R)inf{x|P(R≤x)≥α}　=F-1R(α)(1)。α∈(0,1),F-1R(α)RFR=P(R≤x),inf{·}。(1):VaRRα-,100(1-α)%VaRα(R)VaRα(R)α。(1)VaR,。,VaR。t-1Ψt-1,(1-α),tVaRα-:VaRa,t(Rt)inf{x|Pt-1(Rt≤x)≥α}　=F-1Rt(α|Ψt-1)(2)(2)F-1Rt(α|Ψt-1)RtFRt(x|Ψt-1)=Pt-1(Rt≤x)(:Ft(Rt)),Rtα-;Pt-1(·)Ψt-1。(2)VaR。()VaR,VaR:VaRα,t(Rt)=μt-z1-ασt(3)μt,σt,z1-α(1-α)-。(3)σt,GARCHSV,、t,MoranaGARCHVaR[1];SVVaR,GARCHVaR[2]。,:,(3)VaR。,(2)RtFt(Rt),S,α-F-1α,t(Rt);M,Mα-F-1α,t(R(m)t),(m=1,2,…,M),VaRVaRα,t=1M∑Mm=1F-1α,t(R(m)t)(4)。三、投资组合动态VaR风险度量()N,Rt=(R1,t,R2,t,…,RN,t)′,,:Rp,t=X′tRtMorganRiskMetrics,EWMA—。,,;,EWMA—∑t;,VaR:VaRα,t(Rp,t)=μp,t-z1-ασp,t　=X′tμt-z1-αX′t∑tXt(5)RiskMetricsVaR:;—∑t“”。,ICAVaR。()ICAVaR,。ICA41:VaR,。ICA[3-5],ICAVaR:1.寻找独立成分。Rt,、U,ICt=U·Rt(6)IC=(IC1,t,IC2,t,…,ICN,t)′,ICi,t(i=1,2,…,N)N,ICi,tICj,t(i≠j);U。U。—,HyvärinenOja(FastICA)U[6],Hyvärinen[7]。2.估计边缘条件分布函数。VaR,,Hansent(ARCD)[8]。ARCD,,:PremaratnePearsonIV[9];YanChoi,JohnsonSU(JSU)[10-11]。Z,JSUZ,:X=ξ+λsinhZ-γδ(7),X～JSU(ξ,λ,γ,δ)。ξ,λ(λ0),γ、δ(δ0)。JSUX,sinh(·)sinh-1(·),:G(x,ξ,λ,γ,δ)　=Pr(X≤x)　=Prξ+λsinhZ-γδ≤x　=Υγ+δsinh-1x-ξλ(8)Υ(·)。(7)(8)、JSU、。Yan:,GARCD(p1,q1;p2,q2;p3,q3)-JSU;;[12]。GARCD(p1,q1;p2,q2;p3,q3)-JSU:yt-μt=εt,εt～JSUt(0,ht,γt,δt)ηt=h-1/2tεt,ηt～JSUt(0,1,γt,δt)ht=α0+∑q1i=1αiε2t-i+∑p1i=1βiht-iγt=c0+∑q2i=1ciηt-i+∑p2j=1cq2+jγt-jδt=d0+∑q3i=1diηt-i+∑p3j=1dq3+jδt-j(9)。μt,ht,ξt,λt[10-11];εt,ηtεth-1/2t;JSUt(·,·,γt,δt)JSU,γt,δt。3.利用MonteCarlo模拟计算投资组合VaR。(9)gi,t(ICi,t;ξi,t,λi,t,γi,t,δi,t),N:gt(IC1,t,IC2,t,…,ICN,t)=∏Ni=1gi,t(ICi,t),N:ft(R1,t,R2,t,…,RN,t)　=abs(|U|)·gt(IC1,t,IC2,t,…,ICN,t)　=abs(|U|)·∏Ni=1gi,t(ICi,t)(10)abs(·),|·|。NFt(R1,t,R2,t,…,RN,t)。(10)Ft(R1,t,R2,t,…,RN,t)NS,:(R1,t;1,R2,t;1,…,RN,t;1;R1,t;2,R2,t;2,…,RN,t;2;…;R1,t;s,R2,t;s,…,RN,t;s)Ri,t;ji;t;tij;(Rp,t;1;Rp,t;2;…;Rp,t;s),Rp,t;j=X1,tR1,t,j+X2,tR2,t,j+…+XN,tRN,t,j。(Rp,t;(1);Rp,t;(2);…;Rp,t;(s)),Rp,t;(j);t;tj。42,α-F-1α,t(Rp,t)。M,Mα-F-1α,t(R(m)p,t),(m=1,2,…,M)VaRVaR(p)α,t=1M∑Mm=1F-1α,t(R(m)p,t)(11)。(p),(m)m;F-1α,tα-。四、实证研究():———。:2008122008331(,T=57),:(ZXZQ)、(ZXZQ)、(FYBL)、A(WKA)、(ZGCB),37.26%。,:U=　26.69-8.01　17.78-9.58-3.68-2.53-31.32-14.46　29.79　20.48　7.24　28.23-24.40-8.56　3.02-30.38　28.41-2.13-14.67　27.03　24.06-7.64-12.01-30.89　6.32。1。1,,ZGCB;,IC4。,VaR。1　、()(%)　　J-B()1ZXZQ183749000.008.89-0.0089　0.0416-0.2484　2.6211　1.0648　　(0.5872)2ZXZQ172215000.008.33-0.00330.03690.01842.44360.9673(0.6165)3FYBL155020000.007.50-0.00540.03660.03013.37120.1560(0.9250)4AWKA149746700.007.24-0.00230.03840.16072.79320.4463(0.8000)5ZGCB109596000.005.30-0.01340.0444-0.66824.21486.5973(0.0369)＊＊6IC1——————-0.23621-0.49722.69912.5523(0.2791)7IC2——————-0.139510.05592.94960.0836(0.9591)8IC3——————-0.047310.13791.95483.0662(0.2159)9IC4——————-0.14161-1.74039.0335102.9600(0.0001)＊＊＊10IC5——————-0.13681-0.40383.16511.4485(0.4847)　　:J-B;＊、＊＊、＊＊＊10%、5%、1%。()VaREWMA、MGARCH、ICAVaR,。1.EWMA模型法。MorganRiskMetricsEWMA:　　Ht=(1-w)Rt-1R′t-1+wHt-1(12)-。Bollerslev(1988)GARCH,,α。,RiskMetricsw=0.94。Ht,[Xt=(0.24,0.22,0.20,0.19,0.14)′Xt=(0.2,0.2,0.2,0.2,0.2)′],VaR,12。2.MGARCH模型法。EWMAHt,MGARCH。,:、。Engle(dynamicconditionalcorrelation)[13],DCC-GARCHHt。Ht,VaR,12。3.ICA法。ICAVaR:,,43:VaR;,,p1=q1=1;p2=q2=1;p3=q3=1,(2007)GARCD-JSU2,2ht,γt,δt;,MonteCarloVaR。s=1000、M=500,Ft(R1,t,R2,t,…,RN,t);,α=1%α=5%α-F-1α,t(Rp,t);(11)VaR(p)α,t,3、12。2　GARCD-JSUIC1IC2IC3IC4IC5β0　　　0.0021　　　0.0944　　　0.0263　　　0.0456　　0.0320β10.05850.05730.00080.17310.2259β20.94150.64800.73590.61090.6823C00.01480.0200-0.00390.00790.0065C10.12670.14530.13210.15690.1347C20.63320.60220.48810.36320.5744d00.99481.01101.01001.02181.0108d10.10090.11110.09720.10710.1068d20.61380.58200.72330.42640.6566lnL-79.17-79.17-79.17-79.17-79.173　VaRα=5%α=1%α=5%α=1%2008-01-03-0.0163　0.0020-0.0159　0.0040-0.0146　0.0020-0.0155　0.00392008-01-040.01780.00220.01710.00350.01820.00210.01770.00342008-01-050.02310.00210.02230.00370.02660.00210.02610.00382008-01-060.00630.00240.00630.00370.00180.00220.00140.0036……2008-02-150.00350.00200.00240.00440.00250.00220.00150.00372008-02-18-0.02390.0023-0.02540.0042-0.02310.0023-0.02400.00332008-02-190.02790.00250.02720.00390.02790.00230.02650.00392008-02-200.00920.00210.00830.00460.00720.00240.00610.00392008-02-21-0.03920.0021-0.04020.0042-0.03940.0022-0.04080.0043……2008-03-260.00480.00220.00460.00350.00260.00240.00130.00372008-03-27-0.02340.0024-0.02490.0038-0.02150.0020-0.02300.00402008-03-280.05950.00220.05820.00400.05820.00220.05680.00412008-03-31-0.04170.0021-0.04310.0038-0.04290.0025-0.04400.0042　　:①。②。1　VaR