GARCH H VaR CVaR
VaR VaR VaR VaR VaR VaR CVaR VaR VaR VaR CVaR CVaR VaR CVaR VaR x c 95% p 1 c VaR VaR c c xf ( x) dx VaR VaR VaR VaR VaR VaR VaR VaR VaR VaR CVaR E[ X X VaR] xf ( x) dx / f ( x) dx CVaR
CVaR VaR c 95% CVaR 5% CVaR VaR CVaR VaR VaR CVaR p VaR p * VaR M N p * p * N / M * * B ~ ( M, P ) H p p H p p * LR p p p p 0 : * M N * N M N N ln[(1 ) ] ln[(1 ) ] LR x (1) 3.841 0.95 CVaR VaR CVaR DLC N N 1 1 DLC X i CVaRi N i1 N i1 1 : CVaR X VaR N DLC CVaR VaR VaR VaR VaR GARCH
GARCH GARCH ( p, ) b0 b1 i a a i i j j i1 j1 p GARCH (1,1) p 1, 1, a 1 1 a i j p GARCH ARCH GARCH(1,1) 1 GARCH EGARCH p a a 1 a ln( ) i E( ) ln( ) j j k i1 1 j1 k 1 i k i k GARCH PARCH p i( a 1 a i k ) j j i1 j1 0 i 1,,, 1 i 0 i i
GARCH T GED T d 1 d 1 x ( )(1 ) f ( x) d,( x ) 1 d ( d ) ( ) d d T GED 1 x f ( x) exp (1 ) 1 ( ) 1 1 1 ( ) 3 ( ) 0 GED GED GED PARCH VaR 1 VaR p z 1 c p GARCH z c c z c z CVaR CVaR E[ z z z ] z CVaR c c CVaR E[ p 1z p 1z p 1zc ] p z 1 c CVaR z f ( z) dz 1 c CVaR z zc z 1 1 p 1 p CVaR z e dz e 1 c (1 c) T CVaR
d 1 d 1 ( ) d 1 ( ) d 1 p z 1 c z p 1 d z c CVaR z (1 ) dz (1 ) 1c d ( ) d 1 c ( d 1) d d ( ) d x k 1 k e x dx 0 ( ) GED CVaR p 1 z ex p[ ] zc 1 C V ar z d (1 1 1 c ) 1 ( ) z 1 1 ( ) 3 ( ) Eviews5.0 Mahemaica5 ln( p / p 1) p x 0.95 () 5.991 ADF p 0.061 b 0 b1 7 a a a a a GARCH a F LM 5% GARCH
GARCH EGARCH PARCH VaR p 1 zc VaR CVaR VaR VaR p p p 1 p VaR x x x NORM PARCH NORM GARCH NORM EGARCH NORM EGARCH NORM PARCH NORM GARCH EGARCH EGARCH VaR PARCH GARCH VaR PARCH EGARCH GARCH CVaR CVaR VaR VaR CVaR VaR CVaR zc( 1.645) DLC VaR CVaR VaR CVaR NORM EGARCH NORM GARCH NORM PARCH DLC DLC DLC EGARCH CVaR DLC VaR CVaR
Eviews5.0T d Eviews5.0 @ dis( Z, d) T c d 1 d ( ) ( ) Mahemaica5 d T VaR LR VaR T PARCH EGARCH GARCH x x x TPARCH TGARCH TEGARCH TEGARCH TPARCH TGARCH CVaR DLC DLC DLC T PARCH T GARCH T EGARCH GED Eviews5.0 GED (0, ) @ ged( Z, ) c GED 5 Mahemaica
GED VaR CVaR x GED PARCH x GED GARCH x GED EGARCH GED PARCH GED EGARCH GED GARCH LR GED PARCH EGARCH VaR GARCH CVaR DLCGEDPARCH DLCGEDGARCH DLCGEDEGARCH GED PARCH CVaR DLC T GED PARCH CVaR GED PARCH GARCH VaR GARCH EGARCH PARCH T EGARCH VaR PARCH VaR GARCH EGARCH GARCH T GED CVaR VaR CVaR GED PARCH CVaR PARCH VaR CVaR