期貨最優(yōu)套期保值比率估計(jì)

1、期貨最優(yōu)套期保值比率的估計(jì)、理論基礎(chǔ)（一）簡(jiǎn)單回歸模型（OLS）考慮現(xiàn)貨價(jià)格的變動(dòng)（S）和期貨價(jià)格變動(dòng)（F）的線性回歸關(guān)系，即建立：.*.一St=chFtt其中C為常數(shù)項(xiàng)，5為回歸方程的殘差。上述線性回歸模型常常會(huì)遇到殘差項(xiàng)序列相關(guān)和異方差性的問題，從而降低參數(shù)估計(jì)的有效性。（二）誤差修正模型（ECM）:Lien&Luo（1993）認(rèn)為，若現(xiàn)貨和期貨價(jià)格序列之間存在協(xié)整關(guān)系，那么，最優(yōu)套期保值比率可以根據(jù)以下兩步來估計(jì)。第一步，對(duì)下式進(jìn)行協(xié)整回歸：St=abFtt第二步，估計(jì)以下誤差修正模型:m6=：(&-Ft)二Ft、5i=1式中P的OLS估計(jì)量白即為最優(yōu)套期保值比率h（三）

2、ECM-BGARC峽型：分為常數(shù)二元GARCH1型和D-BEKKGARCH型。其均值方程相同，為(2-8)一&S1C1%"】I=1+1+F一G一必z一一D（其，J=S4-C?+酢u）即上文提到的誤差修正項(xiàng)）%一N(0,Ht)（四）期貨套期保值比率績(jī)效的估計(jì)我們考慮一包含1單位的現(xiàn)貨多頭頭寸和h單位的期貨空頭頭寸的組合。組合的利潤(rùn)AVh為:Vh=CsSt-CfFt(2-10)套期保值組合的風(fēng)險(xiǎn)為：_2_2_Var(Vh)=C：Var(S)C：Var(F)-2CsCfCov(S,F)(2-ii)由于現(xiàn)貨的持有頭寸在期初即為已知，因此，可以視之為常數(shù)，等式兩邊同除c2,得：Var(

3、2VH);Var(S)(h*)2Var(：F)-2h*Cov(S,F)(2-12)Cs對(duì)于不同方法計(jì)算出的最優(yōu)套期保值比率h*,我們可以通過比較(2-12)來對(duì)它們各自套期保值的保值效果進(jìn)行分析。二、實(shí)驗(yàn)?zāi)康睦蒙鲜隼碚撃Ｐ凸烙?jì)中國(guó)期貨交易所交易的期貨合約的最優(yōu)套期保值比率并對(duì)保值效果進(jìn)行績(jī)效評(píng)估，說明期貨套期保值在經(jīng)濟(jì)生活中的重要作用，并找出績(jī)效評(píng)估最佳的套期保值比率模型。三、實(shí)驗(yàn)過程(一)數(shù)據(jù)的搜集、整理實(shí)驗(yàn)所用的期貨數(shù)據(jù)均來自上海期貨交易所，現(xiàn)貨數(shù)據(jù)(Au9995)為均來自上海黃金交易所。由于期貨合約在交割前兩個(gè)月最活躍，所以每次取期貨合約時(shí)都只用它到期前倒數(shù)第二個(gè)月的數(shù)據(jù)，現(xiàn)貨數(shù)據(jù)與期

4、貨數(shù)據(jù)按時(shí)間對(duì)應(yīng)。Vorkfile:HR-(c:docu>en1:sandsetti>B.口X醐ew|PQ匚|01怕士|PfG”宓匚吐仁+J一|Show|SUre|Delete|G&nr|5anple|Range:1243-243or)sDisplayFilterSample:1242-243ot)sVUnOtledkNewFge/（二）用OLS模型估計(jì)最優(yōu)套期保值比率1 .調(diào)整樣本期Torkfile:HR-(c:docu>eiftsandsetti<B.一口XTie科|Pr口匚|obje±Priril:|5”曰L>eBi4+J-|5hQW|F曰

5、tchSUreDetete|Gen|5日叩1日Range:1243-243or)sDisplayFilter.'Sample:2242-242obs<Urrtftled/NewPage/可因2 .建立F和S的差分序列Tnrkfile:HK-(c:docu>eiftsand.setti.»"if叫Prw|obje比|PfE”SaveDeEik+HShow|FgtchStore|Detete|G&fv5事昨>仁|DisplayFiIter.Range:1243-243obsSannple:2243-242obsdSI<UMrtled/Ne

6、wPage/3 .建立AF和AS的OL響單回歸模型DependentVariable:ISMethod:LeHstEqere審Date06/Oan3Time-13:31Sample:2243Includedobservations:342VariableCoefficientStd.Errort-StatisticProh.cO.0C12800.0711730.0179910.9357IF0.8620350.02204239.108210.0000R-squared0.9C4365Meandependenlvar0.024256AdjustedR-squared0.963500S.D.depe

7、ndentvar2ggggeBS.E.ofregrassiciri1JC7155Akaikeiiifocriterian3049594Sumsquaredresid2S41IQO0Schwarzcriterion3.078520Ldqlikelihood-367.0130Hannan-Quinncriter.3.061309F-statistic1529452Durbin-Watsonstat2743740Frob(F-statistic),000000上述結(jié)果寫成方程式為:ASt=0.001280+0.862035AFt+tt(0.017991)(39.10821)P(0.9857)(0.0

8、000)該結(jié)果顯示方程整體上是顯著的，而且解釋變量的系數(shù)很顯著(P值為0),故基本上認(rèn)可該回歸模型。回歸結(jié)果表示每一單位的現(xiàn)貨頭寸要用0.862035單位相反的期貨頭寸進(jìn)行對(duì)沖,即最優(yōu)套期保值比率為0.862035。(三)用ECM模型估計(jì)最優(yōu)套期保值比率1 .期貨價(jià)格序列的平穩(wěn)性檢驗(yàn)Date:06/配力3Time:13:37Sample:2243Includedobservations;242AuiocoirelationPartialCorrelationACPACO-StatProb11111111111111111II111111111111III11I11匚11101|11IIIIII

9、u110.9600.960225.73000070.9230.090437.790,00030,696-0.01563B,210,00040.8600.00B822.19O.ODO50.S410.057g犯310,000£0.G1G001011G5.10000707960038132420000W0.769-0.0S01473.30,000S075100911616.200001i00.730-00191751.90,000110,702-0,1051677.90.000120.677-00121995.40000130,640-0,1352101.20000140.C12a,043

10、2196.20.000150,5900.0B422B8.30.000160.664-0081237180000170.54500732449.90000160.522-00452521.6000019D.49S-0.04725S7.30.00021004680,0672645.00000210436-00732696.500D0220405-0025274040000230.360-0074277660000240.3+20.0S52S0G.20,000n1111111111111JJJJ"111II1Biiii了JiJiiiiiii小序列的自相關(guān)系數(shù)(AC)沒有很快趨近于0,說明原

11、序列是非平穩(wěn)的序列以下進(jìn)行單位根檢驗(yàn)UnitEootTestNullHypothesis；FhwsunitrootEKogeng里Constant,LinearTrendLagLength:0(AutornaticbasedonSI*hW*LAG=14)i-StatisticPrch*Augm曰口帕。Dick日y-FullTrjewtstatistic-2.241594口463gTestcriticalvalues,1%Iffvel-3.9964315%1覬色-34285010%level-3.137665*Wackinncin(190S)orie-sidcdp-values.從結(jié)果可以看出A

12、DF檢驗(yàn)值大于各顯著水平臨界值，且犯第一類錯(cuò)誤的概率大于0.1,說明我們不能拒絕原序列存在一個(gè)單位根的假設(shè)。接下來對(duì)原序列的一階差分序列進(jìn)行檢驗(yàn)。NullHypothesis:D(F)hasaunitrootExasjenous:Gonstarit,LinearTrendLagLength:0AutomaticbasedonSIG,MAXU<G=14)t-StatisticProb*滴'_1口面白口蛆4。企1<藥-£川1臥怛包伯1伯11£：-篁,15與9白SMgTestcriticalvalues:1%level3gg65g25%level-3.4255

13、9110%level3.137711*MacKinnon(19SE)one-sidedp-values.從該結(jié)果看出ADF統(tǒng)計(jì)量小于臨界值，犯第一類錯(cuò)誤的概率接近為0,說明一階差分序列不存在單位根。綜上，我們可以肯定期貨序列F是一階單整的2 .現(xiàn)貨價(jià)格序列的平穩(wěn)性檢驗(yàn)Date：05/DEH3nme:13:40Sample：2243Includedobervaticins:242ACPACQ-StatProbAulocorrelationPartialCorrelaticnI11uII|i20,931I30,896II140.670I150.644II1eo.ewI1T0.796II180770

14、I1IIS0751II1100.729匚1110.69611120.66Sc1130.63C111140.69S11150,571111160.5431;l>170.521l1160.494II1190.46SII1200,442t1210,41211220,393lII230.3461:1240.324096?23680D0000.074440.110,000-D.042639.17O.00D0.060827.050,0000.0211004.70000-0J251172.0000003551331.10,000-0.0521480.90,0000.0691021.00,000-0.0

15、321759.20.000-0.1401883.30000-0,Q051398.90.000-0.1402101.40,0000.03721S150,00000452279.30,000-0.04723562O.00D0.090242750.000-OOE7249200000-00492550200C00.0182602.10,000UQ922547AQ.QOO0.0092SB67O.OCD-OBED2719.00.0000.1142747.500C0NullHypottiesis:ShasaunitrootExogenous:Constant.LinearTrendLagLength:口(A

16、utomaticbasedonSIC,M>X1JG=14)t-SlatietitProh*AugnnenteclDlckey-Fjllertest匚-2J510500.5139Testcriticalvalues:1%level-315%level-34Z650310%lerel3.137565*WacKinnon(1696)one-sidedp-valuesNullHypottieeie:DCS)hasaunitrootExagenoue:Constant,LirearTrerdLagLength:0(AntamaticbasedonSIC.MAXLAG=14)1-StatisticP

17、robTAugmentedDickey-Fullerteststatistic-1701352O.OUOOTestcriticalvalues:1%level5%level10%level-3.996592-3.420501-31377rli*WacKlnnon(1996)one-sidedp-values.可以發(fā)現(xiàn)現(xiàn)貨價(jià)格序列也不平穩(wěn)，它與期貨價(jià)格一樣也是一階單整的。由于S和F都是同階單整的，所以滿足協(xié)整檢驗(yàn)的前提。3 .對(duì)現(xiàn)貨價(jià)格序列S和期貨價(jià)格序列F的協(xié)整檢驗(yàn)用現(xiàn)價(jià)對(duì)期價(jià)做回歸，用其殘差來檢驗(yàn)期貨價(jià)格序列與現(xiàn)貨價(jià)格序列是否存在協(xié)整關(guān)系。DependentVariabia-NEIiqcI:

18、LeastSquaresDate:06/08113Time:13:42Sample:1243includedobsenrations:243VariableCoefficient8td.Errort-StatisticProbC14,462672.1703696.6621550.0000F0.S524070.C06385149.B2370.0000R-squaredO.S8S36QMeand&perlentvar339.0907AdjustedR-squaredo.ges3O5SD.de|>erideritvar11口6口46SE.cfregrGssiori1.143813Aka

19、ikeinfocriterior3.114809Sumsquaredresid315.3025Schwarzcriterion3.143558Loglikslihood-37B44Q3Hannan-Quinnchlor.3.1263IS9F-statistic22387.20Durbin-Batsonstat0.598391Prob(F-statistic)O.OOCOOO以上的t、F統(tǒng)計(jì)量都可以認(rèn)為模型是顯著的。保存該模型，再進(jìn)一步對(duì)其殘差進(jìn)行單位根檢驗(yàn)。將殘差保存到新序列e中。NullHifpothesis:EfiasaunitrootExogenous'NoneLagLength

20、-1(Autarnaticb3sedonSIC.MAXLG=14)bStatisticProb.*1ALiqnnEHted口記ke，F(xiàn)ulle怕名istatiM讓七二0244U燦00Testcriticalvalues:1level-2.5745935%level-1,34214710%level1,615621MacKinnari(19SS)une-sidcdp-values.結(jié)果顯示，在1%的置信區(qū)間內(nèi)可以接受殘差序列e不含單位根的假設(shè)。這說明兩序列協(xié)整關(guān)系存在，因此這里的殘差項(xiàng)e可以當(dāng)做誤差修正用作建立誤差修正模型。4 .建立含有誤差修正項(xiàng)的F和S之間的誤差修正模型Dependentva

21、riable:ISMethod:LeastSquaresDate:06/06/13Time:13:46Sample:2243Incluidedobservations:24iYariwb帕CoefficientSid.Errort-StatistiQProb.C00006940.062673-0.009314o.sa2eIF0892353001974345.1S9910.ID000田)0.4691BO0055073-93572E30.0000R-squaredO.0S52S6Meandependertvar0.024256AdiustedR-squared0,894389S.D.depende

22、ntvar2.939985S.E.ofregression0974931Akaikeinfocriterion279S419Sumsqusredresid2271671Schwarzcrilerion2.347670Loglikelihood3357296Hannan-Quinricriter.2816842F-atarisilt1021.490Durbin-Watsonstat2205319Prob(Fjstatistic)0.000000故協(xié)整回歸方程式為:ASt=-0.000584+0.892353AFt-0.469180ECM-1+t(-0.009314)(45.19891)(-8.3

23、97263)P(0.9926)(0.0000)(0.0000)從F統(tǒng)計(jì)量看出該方程整體上是系數(shù)顯著的，自變量系數(shù)和誤差修正項(xiàng)系數(shù)的t統(tǒng)計(jì)量都很顯著，故該回歸模型擬合得較好?；貧w結(jié)果表明每一單位的現(xiàn)貨頭寸要用0.892353單位相反的期貨頭寸進(jìn)行對(duì)沖，即最優(yōu)套期保值比率為0.892353,這比簡(jiǎn)單的OLS模型估計(jì)出的結(jié)果0.862035稍大。(四)用ECM-BGARCH1型估計(jì)最優(yōu)套期保值比率1.ARC做應(yīng)檢驗(yàn)HeterosKedasticit/Test：ARCHF-statisticObs*R-squared4.959913Prob.F(3,236)U.231EBProb.Chi*Square

24、(3)0.00230.002STestEquation'Depend9ntVariable:RESIDESMethod:LeastSquaresDste:06J09f13Time:13:52Sample(adjustsd):5243includedobsenrations:239afteradjuslnnentsC3.7762760.161149£,1259700.0000RESID”(-1)0.249211口.065267,0163490.0002RESICT2H)-0.048040067773-0.7171510.474URESIDA2(-3)-0.0230310.085

25、976-0.34907807273R-sci(jarad0.059548Meandependentvar0.941907AdjustedR-squared0.047542S.D.dependentwair1930789S.E.cfreoression1364333Akaikeinfocriterion4.121520Sumsquaredresid6344173Schwarzcriterion4.179303Loglikeliliood-4385330Hannan-Quinncriler.4.14506&F-fftatlatic4959913Durblrt-Wateonstat19967

26、2aProb滬與匕tiwtic)0.002343VariableCoefficientStd.Errort-StatisticProb,可以看出，F(xiàn)統(tǒng)計(jì)量和LM統(tǒng)計(jì)量(Obs*R-squared)都是顯著的，這說明方程殘差項(xiàng)具有ARCH效應(yīng)，故可以建立ECM-BGARC根型。鑒于我編程基礎(chǔ)較為薄弱，以下只建立常數(shù)相關(guān)系數(shù)二元GARCH真型，而D-BEKKS型則不予考慮。2.常數(shù)相關(guān)系數(shù)二元GARC版型對(duì)AS做單方程的GARCH古計(jì)Dependentvariable:ISMethod;ML-ARCH(Marquardt)-Norm31distritutionDate:06/06/13Time:1

27、3:53Sample!2243Induidedobservations:247Conrgenceacrilavgdafter19IterationsPresamplevariance;(r白日rnte二D.7)GARCH=C(4)十CC5)"RESID(m十C(E廣GRRCH91)VariableCoefficientStdErrorz-StaflsticProbC0.0146070.09031S0,242155o.eoe?IF090461700192564B.9772800000-0406Q130.059649-6.9315600.0000VarianceEquationc0.36

28、79720.210300412714200000RESID(-1)A20171S7D0.07559022451700.0249OARQHCD-0.10S0500.226803-0.4808110.6307R-squared09Q43B4Meandependertvar0.024266AdiusteelR-squared0993500SD.depandentvar299S966S,E.ofregression0979024Akalkoinfocriterion2777499Sumsquaradresid229,0704ScHwaccriterion2064001Loglikelihood-330

29、.0773Hannan-Quinncriter2.812345F-statisiic4Q4.7640Durbin-Watsonstat2.354354Prob(F-statistic)0000000對(duì)AF做單方程的GARCH古計(jì)DependentVariable:IFMethod;ML-ARCH(Marquardt)-NomnaldistributjanDate:06/083Time-13:59Sample!2243Includedobservatloris:242Convergenceachievedafler24IterationsPresanplevariance:timckcast(raramete二D.7)GARCH=C(4)+CgF?E3IDm廣2十C(E廣GRRCHFI)VariableCoefficientStdErrorz-StatisticProbc-0.0112400.061151-0.1S29140.6542IS1009723O.021S1746.0695200000EM)0.447496O.0C47336.912406oooooVarianceEquation00.9855