Granger FIA JOSEPH. Stock index futures 2005

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1 Granger Fuures Indusry Assocaon FIA /3 4 5 FIA JOSEPH Soc ndex uures 5

2 oon 974. erec mare r 8 9 T mar o mare

3 . F C C F F = C + ( r d)( T ), C = F + ( r d)( T ). r d T C = α + C β c ( C C ) +, C = α + C + β ( C C ) +. c β c β α c α 3 C α β c β c C = + + C α β β c C β c β C C β c β 3 C C 4 C C = α + δ ( C C ) α = α α c, δ = β c β 3 = - β c = β = δ = δ = δ = C C C C Garbade & Slber 983 F C C C GS Garbade & Slber s model F C = F C + C C, 5a 5a, F C = ( r d)( T ) + C C. 5b C = ( r d)( T + ) + C C F. 5c

c β c β α c α 3 C α β c β c C = + + C α β β c C β c β C C β c β 3 C C 4 C C = α + δ ( C C ) + 3.

4 5b 5c 3 F C = β + β( F C ) + 3 = α + ( r d)( T ) δ ( r d)( T ) +. 5d β β = δ. δ = C C 3 3 GARCH 3. GARCH Bollerslev e. al.,99 Engle (98) (Auoregressve Condonal Heerosedasc model--arch) Bollerslev (986) ARCH GARCH Generalzed Auoregressve Condonal Heerosedascy model--garch 3.. ARCH ARCH y x β β x ARCH h y = h( = y Ω, x β., Λ, Ω ~ N( x β, h ),, α), (6a) h,, Λ, h h(,,,, α) = y x β h h = h(,, Λ,, x, x, Λ, x, α) (6b) h = Λ α h + α = α (6c) α >, α, =,, Λ,. 3..GARCH 986 Bollerslev ARCH GARCH GARCH (, ) y h ~ N(, h ), = α + α + β h = α + α( L) + β ( L) h, (7) = y Ω x β., >, α >, α, =,, Λ,, β, =,, Λ,. = GARCH(, ) ARCH () ==, Box & Jenns (976)

. ARCH ARCH y x β β x ARCH h y = h( = y Ω, x β.

5 3. EGARCH 3.. EGARCH GARCH 99 Nelson GARCH exonenal GARCH model EGARCH) 99 Senana (99) 99 Engle GARCH uadrac GARCH model QGARCH) 994 Zaoan TGARCH hreshold GARCH --TGARCH) GARCH GARCH Inh = α + β Inh + α ( θ + γ γe ), (8), >, α, θ, γ, α, =,, Λ,, β, =,, Λ,. α, α, β GARCH EGARCH 3.. EGARCH EGARCH Bvarae Error Correcon EGARCH Model Tse 999 Ramarasad Bhar EGARCH Ramarasad Bhar F S Co-negraon P ( F, S ) Vecor Error Correcon Model--VECM = F = a + α z + b F + c S +, 9 S = a + α z + b F + c S +. = L L Lx = x, L x = x z F S error correcon erm = = Ω ~ N(, H ), a H σ ρσ σ σ ρσ σ, b In ( σ ) α + α ( z ) + α ( z ) + γ In( σ, ) + θ In( e ), =, =,,,. ( z, ) = z, E( z, ) + δ z,, =,. 3 z = σ,,. 4, =

Inh = α + β Inh + α ( θ + γ γe ), (8), >, α, θ, γ, α, =,, Λ,, β, =,, Λ,. α, α, β GARCH EGARCH 3.

6 unauo-correlaed resduals VECM 9 Ω maxmzng he log-lelhood uncon4 Γ l ( Θ) = Γ( v T = { ( Θ) } L( Θ) = In, 5 [( + v) / ] / ) [ Π( v ) ] l H / (+ v) / ± H v. 6 ν Bollerslev, 987 γ volaly sllover γ α α he mare-secc volaly cluserng/auocorrelaons θ asymmerc volaly coecen 4 Ramarasad Bhar Ramarasad Bhar 9 GARCH F = a + α z + b F + c S +, 7 S = a + α z + b F + c S +. 8 MATLAB Mahemaca or Wndows SAS SPSS Economerc Vews TSW 5 5.

6 ν Bollerslev, 987 γ volaly sllover γ α α he mare-secc volaly cluserng/auocorrelaons θ asymmerc volaly

7 5.. lead-lag Herbs 987 S&P5 MMI Cheung & Ng 99 S&P 5 5 ~ 3 Grunbchler 994 DAX 5 ~ Flemng 996 S&P Pzz S&P Soll & Whaley 99 S&P % The Brady Commsson Reor Cascade Theory Grossman Furbush S&P 5 5% 9

8 Hasbrouc 996 Hogan Kroner & Sulan 997 EGARCH Harrs 99 Neal Ramarasad Bhar [] [M] 5 6 [] [J] 36 37~39 [3] [J] 5 [4].. [M]

9 999 [5] Sucle, Charles M. S. Soc Index Fuures: Theores and Inernaonal Evdence (rd ed.) [M]. Inernaonal Thomson Busness Press, 997. [6] Garbade, K. & Slber, W. Prce movemens and rce dscovery n uures and cash mares [J]. Revew o Economcs and Sascs, 983, [7] Tse, Y. Prce dscovery and volaly sllovers n he DJIA ndex and uures mares [J]. Journal o Fuures Mares, 999, 9: [8] Ramarasad Bhar. Reurn and volaly dynamcs n he so and uures mares n Ausrala: An nervenon analyss n a bvarae EGARCH-X ramewor [J]. Journal o Fuures Mares,,?? 9 :?? [9] Maddala, G. S. & C. R. Rao. Sascal Mehods n Fnance [M]. Elsever Scence B. V., 996. [] Flemng, J., Osde, B., & Whaley, R. E. Tradng coss and he relave raes o rce dscovery n soc, uures, and oon mares [J]. Journal o Fuures Mares, 996, 6: [] Pzz, M. A., Economooulos, A. J., & O Nell H. M. An examnaon o he relaonsh beween soc ndex cash and uures mares: a co-negraon aroach [J]. Journal o Fuures Mare, 998, 8 3 : [] Soll, H. R. & Whaley, R. E. The dynamcs o soc ndex and soc ndex uures reurns [J]. Journal o Fnancal and Quanave Analyss, 99, 5: [3] Hogan K. C. Jr., Kroner, K. F. & Sulan, J. Program radng, non-rogram radng, and mare volaly [J]. Journal o Fuures Mares, 997,7 7 : [4]Waler Enders. Aled Economerc Tme Seres [M]. John Wley & Sons, Inc.995. [5]Maddala, G. S. & C. R. Rao. Sascal Mehods n Fnance [M]. Elsever Scence B. V., 996. [6]Bollerslv, T. Generalzed auoregressve condonal heerosedascy [J]. Journal o Economercs, 986, 3: [7]Engle, R. F. ARCH Seleced Readngs [M]. New Yor: Oxord Unversy Press, 995. [8]Engle, R. F. & Granger, C. W. J. (987). Co-negraon and error correcon: Reresenaon esmaon and esng [J]. Economerca, 987, 55:

Journal o Fuures Mares, 999, 9: 9 93. [8] Ramarasad Bhar. Reurn and volaly dynamcs n he so and uures mares n Ausrala: An nervenon analyss n a bvarae EGARCH-X ramewor [J]. Journal o Fuures Mares,,?

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