1、 l : 2005null08null29T e : (1946null) , 3 , ao , b v 6 5 q , p V 3 = ; (1978null), o , E , b v 6 5 p V 3 bo q $ # Z 宋逢明, 江null 婕( b v 6 5 , null 100084)null null K null 1 : 本文论述了迄今国际文献中关于波动率度量模型的主要理论和实证结果, 概括了度量事前预期波动率的参数模型 (包括离散模型和连续模型) 和度量事后实际波动率的非参数模型 (包括ARCH滤波和平滑子模型和 null已实现 波动率模型) 的特点及统计推断性质, 比
2、较了模型之间的优劣之处, 展望了波动率度量模型的未来研究趋势b1 o M : 波动率度量; 参数模型; 非参数模型; ARCH滤波和平滑子模型; null已实现 波动率模型 m s | : F830 null null null D S M : Anull null null c I | : 1004null4892(2005)06null0001null06一a概null 述o q 6 d 1 M , g F 4 a N ( 3 3 ) # B 5 7 o q bo q 9 V + E M 9 L H 9 6 K 5 B b 1 Engle ( 1982) ARCH , v 9 6 D H
3、M o q , ? Z a o q b“ - , o q X ? Z B v 8 “ , ARCH o q( Stochastic Volatility, / e SV) X d % b v y E nullS : (Mies Von der Roche) : null * c % , | i “ / Z E , C n ! n C b V 0) , 9 $ Andersen, Bollerslev, Diebold Labys ( 2001) 1 BarndorffnullNielsen Shephard ( 2002) 2 L = o q (Actual Volatility)b = 5
4、5 3 o q ( Expected Volatility) Q , Y - o q ( H W W h 0)b i B L o q V ?Z bV , K V i H W W o q , V 7 B 1 Q ! H o q ( Instantaneous Volatility) , BarndorffnullNielsen Shephard ( 2002) 9 H o q ( spot volatility)b o q V H W = 0) ( h #0) : 1 ARCH SV , “ Y - o q ; 7 B s Z T ,“ H o q b“ N , B + Y Z E , c o
5、q ( Implied Volatility) b c o q 1 N # N K M Z “ w o q b Z E K 1 BlacknullSholes c o q , L S N V T V F b , T l m q V M GARCH ( p, q) , l mq i V GARCH ( p, q) ; , T l m q ( V M GARCH ( p, q) , F i V M GARCH ( p, q)bDrost# Nijman ( 1993) 7 , Nijman# Sentana ( 1996) 8 4 GARCH i m % 5 b GARCH , o q $ d Z
6、 L , L H ( / 5 ) b , L i H q , 6 c l A , K GARCH a , o d d 9 w bMeddahi 4 Z 1 B o ( SquarenullRoot Stochastic Autoregressive Volatility, SRnull2财经论丛null 2005年第6期SARV) 5 5 4 B H % o bK , Meddahi Renault ( 1996, 2004) 9 10 , X ARCH J b SV i . , f 4 p , d 9 w Z E , v , R b ( 2005) “ - SV 9 Z E Z F b7 A
7、RCH “ G V 4 M , y N V . d v E , v Z L d 9 w , ARCH L = T b 6 B 4 OU V U o q V bGallant Tauchen ( 1997) , Andersen Lund ( 1997) , Eraker, Johannes Polson ( 2002) , AndersenBenzoni Lund ( 2002) L V t 1 . d y v , ? a m l m q l q b “ - , V Y 0 , T K 7 b L = , P “ , N V i A K 7 bB t 1 1 4 (9 ) l m ( ) $
8、N , V 7 3 N K7 , K 7 V I Andersen Bollerslev ( 1998) # Andersen, Bollerslev, Diebold Vega ( 2002) , K 7 i d ! _ V I Johannes ( 2000)b 6 , 1 c o q D ( V N | 1 l m s g ) 9 | K 7 q l m q s 1 b 8 V I Bakshi, Cao Chen ( 1997)b H W s Z , F ; 7 K 7 s Z , K 7 V F bB N V F M 1 K 7 L F B K 7 s , K 7 a H M Z /
9、 K 7 s b o q 9 G + L ! b , Merton ( 1976)4 B e K 7 , ( o “ , null ( t) null, ( t) , K 7 V V s , ( Z nullk null2k, 5 o q null2h+ hnull2kb y V U ,3宋逢明等null 波动率度量模型研究的回顾及展望K 7 L bK L Andersen, Benzoni Lund(2002) , Duffie, Pan Singleton ( 2000) , Eraker Johannes Polson ( 2002) , Pan ( 2001) , # Eraker(
10、2001)b t v . d y S o q V U E , ! “- B i n b 6 B K Z _ = l m q “ , o q V d Gaussian OUV , B e _ Levy K 7 z ( BarndorffnullNielsen Shephard, 2001)b K O / , y o q = H F 9 V , V i Q 7 b Z E L = 7 S , M 1 ? Z V INguyennullNgoc Yor ( 2002)b三a非参数模型d Y l m q ( “ F%) l o q b z , L + f T V L = o q 4 Y N b 4 H
11、 W W h , 9V s v : ARCH r o 0 ( ARCH Filters and Smoothers) ; X L C o q ( realizedvolatility)bARCH r o 0 H o q ( h#0) , G “ : r o H Y t (%= t) , 7 0 H Y t (% t)bX L C o q 5 % H W W ( h 0) L = o q bV $ A = u Y : H o q r o(ARCH r o 0 ) L l | “ W 4 (H K ) ; X L C o q 5 L % | “ W 4 ( H K )b1. ARCH滤波和平滑子b
12、 ARCH “ | o q M 4 l m q f , B H q b 7 , Nelson ( 1992) 12 4 , V d i l d , A B 4 | 1 . H o q r o b L N “ H o q V H , P | “ q h 0 f T ! p , B a ARCH , o q , | H ( h#0 H ) H o q B 9 b , V “ Z 9 b B “ , dp ( t) = null( t) dt+ null ( t) dW ( t) , “ Z 9 h#0 n# % / ? B 9 H o q b 9 r B V Y V l m q Z H H F (
13、 , P B “ ARCH r o 0 ( Nelson ( 1992) , Fornari Mele ( 2001) , Mele Fornari( 2000) )bGARCH ( 1, 1) r o T “ Z 9 , H Yt l | “ W “ l m q Z K F ( b : c ( H W W h #0 4 n # % ) Y V B v ( l m q | “ q Z l m q 4 H / ) L C bEGARCH T r o , 9 ? B “ 4 H o q B 9 b ARCH V T H o q B r o , 1 3 r 5 bTaylor ( 1986) Sch
14、wert ( 1989) 4 T H q s , l m q F Z 1 l m q Z F r bKitagawa ( 1987) 4 K d L 4 | r o r q 5 , V t d L r o H # s 9 ARCH r o o q 9 H e B 9 bK , Nelson# Foster ( 1994) Nelson ( 1996) 13 4 r o v s , 5 s $ bARCH r o | 4 | H o q “ K N l m q b7 v K 4财经论丛null 2005年第6期ARCH 0 ; c 9 c l m q (Nelson, 1996)b y K AR
15、CH 0 X | Kalman r o Z Kalman 0 ( Andersen Moore, 1979)bs 0 B v s O B (Foster Nelson, 1996) 14b2. 已实现波动率bX L C o q L D l m q N a Y “ Z T o q 9 b1 Poterba Summers ( 1986) , French, Schwert Stambaugh ( 1987) , # Schwert ( 1989) l m q 9 Z , Schwert ( 1990) , Hsieh ( 1991) ,# Taylor Xu ( 1997) , = 9 l m
16、q Z bX L C o q Z E z y g 4 P K l H W W ( h#0) “ l m q t k ( n# % ) L = V ,y N I n % W ( h 0) o q bX L C o q V l A , l m q V % W h = “ b 4 B H W W h o q Z E b 5 % H W W “ Z 9 T e d o q 9 4 , 4 o q i H M b V |“ Z = M , V ? z N t Z E bX L C o q X V , D F , 1 Andersen, Bollerselv, Diebold Labys( 2001) ,
17、 BarndorffnullNielsen Shephard ( 2002) , # Comte Renault ( 1998)b/ B / X L C o q 9 d 9 bn 5 , T l m q V Z V O ( , , 5 Y X L C o q Y - o q 9 b , , ( L ! K , V T M 1 H W M ( V ? , F B H q S l m q “ q b Q , X L C o q L = o q B d 9 b v k “ , I n . v l K “ b , B Hq / V | e X L C o q T o q y B y $ b L = H
18、 1 I n 5 b i L = v l s G + l m q V , A L = f s bBarndorffnullNielsen Shephard ( 2002) s Levy V z OrnsteinnullUhlenbeckL / bV s V B e l m q nullo q L y , 4 X L C o q l o q s b L y O K X $Andersen, Bollerslev, Diebold Labys ( 2001) F L C bMartens Zein ( 2002) L V , % (1 z g F s N ) , X L C o q y Z E 9
19、 S o q y ? v bo q 9 4 . ( N ) Z 9 i bAlizabeh, BrandtDiebold ( 2002) 15 V N o q 9 M N Q Z b V N 9 1 p + s L ! , 7 X L C o q 1 p , y N = b Z 6 B 0 l m q 7 d l m q Z M ( Davidian Carroll, 1987)bX L C o q 5 V + M y ? Z , 1 X B i n H * bV L A , g K | “ q / , ) = g 4 V L ? Z “ - K 1 ( Hasbrouck ( 1996) ,
20、 Dacorogna ( 2001) 16 , Engle Russell ( 2002) )b四a结束语: o q ? Z , V A V 10 M o q t : K V 5宋逢明等null 波动率度量模型研究的回顾及展望 l m q , E K 4 9 , _ P 2 a9 e d ZE b t t A U Z _ : ( 1) 7 ? o q Z E ; ( 2) a L = 6 M / o q y bX L C o q Q Z _ , i v , E L = y p , 1 p K 9 b V n , X LC o q V o q 5 ? Z Z _ b I D : 1 Anders
21、en, T. G. , T. Bollerslev, F. X. Diebold and P. Labys ( 2001) , null Modeling and Forecasting Realized Volatility, NBER WorkingPaper No. 8160. 2 BarndorffnullNielsen, O. E. and N. Shephard ( 2002) , null Econometric Analysis of Realised. Volatility and itsUse in Estimating Stochastic VolatilityModel
22、s, Journal of the Royal Statistical Society, Series B, 64, 253null280, 3 f q , , f . g % : ARCH J . “ d , 1997, ( 1) : 43null46null 4 K , f W . GARCH y # S “ g s J . 5 S , 2003, ( 4) : 68- 73. 5 , f W . : k SV # “ g J . 5 S , 2004, ( 1) : 38- 44. 6 v , R b. o + $ J . 6 , 2005, ( 1) : 76- 81. 7 Drost
23、, F. C. and T. E. Nijman (1993) , null Temporal Aggregation of GARCH Processes, Econometrica, 61, 909null927. 8 Nijman, T. H. , and E. Sentana ( 1996) , null Marginalization and Contemporaneous Aggregation of Multivariate GARCH Processes, Journal ofEconometrics, 71, 71null86. 9 Meddahi, N. and E. Renault ( 1996) , null Aggregation and Marginalization of GARCH and Stochastic Volatility Models, Working paper,Department of Economics, University of Montreal and CIRANO. 10 Meddahi, N. and E. Renault (2004) , null Temporal Aggregation of Volatility Models, Journal of Ec
