* : GARCH 2003~2009 2008 : GARCH : F831 : A 2007 2008 Filardo (2004) 6 Christiano (2007) 2009 (M 2 ) (2009) 30% 10 2008 2009 7 2008 2009 Bernanke and Gertler (1999) Cecchetti (2000) : ; * : (06XNB003); (AHSK09-10D03) 80 /2011.10
MRS-GARCH MRS-GARCH Bernanke and Gertler (1999) ; ; Cecchetti (2000) ( ) Gray (1996) MRS-GARCH (2001) 500 t- Gray t- S t S t S t =1 ; 90 S t =2 Hamilton and Susmelb ( 1994) r t ζ t-1 ~ t μ1t σ 1t! df1 (1) t μ 2t σ 2t df1 Gray (1996) r t pt it μ it σ 2 it GARCH df i t- (i=1 2) ζ t-1 t-1 pt it =Pr { St=i ζ t-1 } GARCH t S i (MRS-GARCH) GARCH (GARCH) r sp t-1 /2011.10 81
r it =a 0i +a 1i r t-1 +a 2i r sp t-1+ε t i.id ε t ζ t-1 ~t μ it σi t df t i=12. (2) : f pt it =π 1t-1 pt it-1 1 f μ it =a 0i +a 1i r t-1 +a 2i r sp t-1 for i=12. (3) 1t-1 pt it-1 +f 2t-1 (1-pt it-1 ) +(1-π 2) (3) ( ) 500 (S&P500) GARCH 2003 1 1 2009 12 15 ( Datastream) 1 {S t-1 S t-2 S 0 } GARCH (1 1) σ 2 it=b 0i +b 1i ε 2 t-1+b 2i σ 2 t-1 (4) t σ 2 t=e [(r t -E [r t ]) 2 ζ t-1 ] =E [r 2 t ζ t-1 ] - {E [r t ζ t-1 ]} 2 (5) =pt 1t (μ 2 1t+σ 2 1t)+(1-pt 1t )(μ 2 2t+σ 2 2t)-[pt 1t μ 1t + (1-pt 1t )μ 2t ] 2 σ 2 t 1 (2003 1 1 2009 12 15 ) σ 2 it+1(i = 1 2) 1 (2) : ε t-1 =r t-1 -E [r t-1 ζ t-2 ] =r t-1 - [pt 1t-1 μ 1t-1 +(1-pt 1t-1 )μ 2t-1 ] (6) S t : Pr {S t =1 S t-1 =1} =π 1 Pr {S t =0 S t-1 =1} =1-π 1 (7) 3 2007 Pr {S t =0 S t-1 =0} =π 2 Pr {S t =1 S t-1 =0} =1-π 2. π 1 π 2 [0 1] 2008 MRS-GARCH (1 1) Λ: T Λ=Σln{pt 1t f 1t (r t ;μ 1t σ 1t df 1 )+(1-pt 1t )f 1t (r t ;μ 2t t=1 σ 2t df 2 )} (8) t pt 1t pt 2t f 2t-1 (1-pt it-1 ) f 1t-1 pt it-1 +f 2t-1 (1-pt it-1 ) f it μ it σ 2 it df i t- (9) 2003 2007 500 82 /2011.10
2008 ( ) 9 1/(1-π i ) S&P500 2003 1 1 2009 12 15 1 1813 323 46 250 GARCH (1 1) 1 MRS- GARCH MRS - 1 GARCH p- GARCH (11) MRS-GARCH a 0 a 1 0.0005 * -0.0045 0.0003 0.0322 0.0659 0.4516 a (3) (4) 2 0.1058 *** 0.0289 0.0009 b 0 0.0000 ** 0.0000 0.0167 5% b 1 0.0849 *** 0.0255 0.0000 b 2 0.9345 *** 0.0127 0.0000 a 1i d f 3.0847 *** 0.6709 0.0000 5000.553 MRS-GARCH 1 ( ) a 01 a 11 a 21 0.0823-0.0287 ** 0.1836 *** 0.1033 0.0492 0.0461 0.4839 0.0498 0.0001 b 01 0.4184 * 0.2228 0.0604 b 11 0.0651 ** 0.0264 0.0137 b 21 0.8508 *** 0.0672 0.0000 df 1 3.0847 *** 0.6709 0.0000 2 ( ) a 01 0.0521 0.0339 0.1238 a 11-0.0051 ** 0.0275 0.0427 r sp t-1 a 21 b 01 0.0935 ** 0.0203 *** 0.0446 0.0072 0.0362 0.0048 1% ( ) b 11 0.0621 *** 0.0076 0.0000 b 21 0.9332 *** 0.0081 0.0000 df 1 4.0775 *** 0.5651 0.0000 π 0 0.9969 *** 0.0023 0.0001 π 1 0.9783 *** 0.0012 0.0000 1 : 322.58 π 1 π 2 1 2 : 46.08 : *** ** * 1 % t-1 t 5% 10% /2011.10 83
(9) 2 MRS-GARCH 1 ( ) (9) 3 2 1 ( ) 2007 2008 3 2003 1 1 2009 12 15 84 /2011.10
2008 9 4 5 2009 5 4 2008 15% 2009 4 2003 1 7 2009 12 M 2 30% 2008 20% 2009 4 2003 M 2 4 5 2009 2009 27.5% 2009 GDP (8.7%) 2009 7 1 3000 34% ( ) /2011.10 85
MRS-GARCH ( ) GARCH 2003 2009 2008 ( ) MRS-GARCH 322 4 86 /2011.10
( ) ( ) : [1]. [J]. 2001 (7) 60~67. [2]. [J]. 2002 (3): 13~20. [3]. : [J]. 2009 (8): 182~193. [4] Filardo A. Monetary Policy and Asset Price Bubble: Calibrating the Monetary Policy Trade-offs [DB]. BIS Working Paper No.1552004. [5] Bernanke B. M. Gertler. Monetary Policy and Asset Price Volatility [J]. Federal Reverse Bank of Kansas City E- conomic Review 1999 (4): 17~51. [6] Cecchetti S. G. Hans L. John and S. Wadhwan. Geneva Report on the World Economy: Asset Prices and Central Bank Policy[R]. Geneva 2000. [7] Christiano L. C. Ilut R. Motto and M. Rostagno. Monetary policy and stock market boom-bust cycle [DB]. European Central Bank Working Paper No. 955 2008. [8] Gray S. F.. Modeling the Conditional Distribution of Interest Rates as a Regime-switching Process[J]. Journal of Finance and Economics 1996 (1): 27~62. [9] Hamilton J. R. Susmelb. Autoregressive Conditional Heteroskedasticity and Changes in Regime [J]. Journal of E- conometrics 1994 (1): 307~333. Abstract: This paper employs Markov Regime Switching GARCH model to examine the nature of stock market volatility in China from 2003 to 2009. Empirical evidence suggests significant regime changes in the stock market volatility ignited by monetary policy adjustment since the new global financial crisis. The results show that the stock market in China has switched to a more volatile period with highly persistent volatility since late 2008. Theses findings indicate that the central bank of China should incorporate stock market volatility into its information set for policy adjustments. Keywords: MRS-GARCH; Volatility; Monetary Policy; Regime Switching /2011.10 87