CFEF RR/4/6
6 * Scaled- VaR Scaled- Scaled- Scaled- Scaled- VaR Kendall(1953) Osborne(1959) 1 1994 VAR Rsk Mercs, Alexander 1961 Osborne * MADIS
Peers 1991 198 1989 S&P5 Peers 1991, Smh 1981 Gray French 199Per 1994 Hsu 198 Gray French 199 Press 1967 Kon 1984 Praez 197 Blaberg Gondes 1974 Gray French 199 Felpe Javer (1997) Scaled- Scaled- Praez 197 Scaled- 1998 ARCH 199 1996 1999 5 9 3 Parean 3 JB 1 3 D Scaled- 1 1 Scaled- suden's dsrbuon (noncenral dsrbuon) Scaled- v
VaR Scaled- Scaled- Scaled- Praez 197 Scaled- 999999 39916 1997 1 1 31 = 1*log( I / ) R I 1 I Monday effecs 1-9.3353 9.415.353 1.6419 -.156 9.16-1.657 9.438.196 1.788 -.4116 8.758 1 6 7 A 1 GB488-85 D D 5 D D n Y Y.5 Y.995 14-35.8 -.91.5 14-34. 1 Logsc Dsrbuon 1/ [ v/( v )] 3 3 Scaled- Scaled- 5 Scaled-
x µ exp( ) f( x) = α x µ α[1 + exp( )] < µ µ < α α > ER ( ) = µ Var( R ) = πα /3 Scaled- α R v + 1 Γ( ) ( ) Scaled- ( ) x µ f x = [1 + ] v Γ( ) π( v ) ( v ) Γ(.) µ < µ < > v R Scaled- v > ER ( ) = µ v+ 1 Var( R ) = 3 Exponenal Power Dsrbuon 1 x µ 1+ β exp[ ] α f( x) = 3+ β ( ) 3+ β αγ( ) < µ µ < α α > < β 1 β 1 β 1< β < β = < β 1 R ER ( ) = µ Var( R ) Γ [3(1 + β ) / ] α Γ [(1 + β ) / ] 1+ β = 4 Mxures of Two Normal Dsrbuons ( x µ 1) 1 1 e, λ π1 f( x) = ( x µ ) 1 e, 1-λ π µ < µ < > λ µ 1-λ µ 1 1
R ER ( ) = µ = λµ + (1 λ) µ Var( ) = λ [( µ µ ) + ] + (1 λ )[( µ µ ) + ] 1 R 1 1 λ [( µ 1 µ ) + 3( µ 1 µ ) 1 ] + (1 λ )[( µ µ ) + 3( µ µ ) ] k = 3/ { λ [( µ 1 µ ) + 1] + (1 λ )[( µ µ ) + ] } 3 3 µ.697578935814.68516743443 1.1155331519 1.1631844579 µ.748563473.78766797465 α.68481651618315.755163161819 µ.83315119364.73391673465 Scaled 1.94858557817 1.8464634866 v.789667775779 3.9769595587577 µ.76169163186.776416718517 α.863899367688.98614459657 β.4141831834.44514841 µ 1.115848733.837613314363 1.7914348815.9455493116337 µ -.6756875673 -.63453863197 1.93777439763166.4441615913617 λ.554188413564.6559188957451 k -.13186585513 -.116448783533 3
1 3 µ.749.78.353.196 1 Scaled.73 3.1 Scaled β.3.4.45 β β = β 1 β 4 k -.7 -.13 (, 9) [ 9, 8) [9, ) ν p ( ν np) ν V = p np n = 1 V ν p 4 n 4 V V 1.555e+13 1.5563e+11 3.44e+3 1.937e+3 Scaled 14.1169 19.999 1.945e+4 5.556e+3 4.9984e+3.1553e+ V 19.5 3.1.1 36. 4.1.5 ( ν np ) V np
ν p n ( ν np ) np 1.e+11 * 1.4838.4..................684 V Scaled-.1 ( ν np ) Scaled- Scaled np.6 4.4313.1384.874.14.164.99.56 1.856.4487.651.6 1.9 1.655.1434.3785 3.345.687 1.169.8153 ( ν np ) 1 np Scaled- (, 9).6 [9, ).8153 VaR VaR Value a Rsk Prob( P VaR) =C C P VaR 5 VaR Scaled- 1% -.54-3.7-4.7651-3.1971-3.961-4.9555 5% -1.7643-1.9416 -.3335 -.55 -.4399 -.4367 1% -1.359-1.498-1.576-1.558-1.6557-1.65 3 6 7 6 VaR
Scaled- 1%.496.381.384.3548.6 5%.759.3.44.1566 -.13 1%.1773.1346.46.886 -.1 VaR VaR Scaled- 5 6 VaR Scaled- VaR 5%Scaled- VaR 5% 1% VaR 1% 7 95% VaR Scaled- VaR 1.9138.913.4941.4.38.496 -.333 -.161 -.8 -.1184 -.67 95% VaR VaR 5% Scaled- VaR -.8% Scaled- 3 Scaled- 8 8 Scaled- Scaled- Scaled- [R,R + S].4376.413.415.4388.4136.415 [R + S,R + S].79.774.797.753.76.816 [R + S, R + 3S].18.16.166.19.189.157 [R + 3S, R + 4S] 5.75e-6..51 6.74e-6.4.45 [R + 4S, R + 5S].33e-9.1.1 3.1e-9.5.17
[R + 5S, R + 6S] 1.14e-13 3.97e-6.1 1.67e-13 3.878e-5.7 Scaled- Scaled- R S 5 [R,R + S] Scaled- Scaled- 8.9 Scaled- 9. 347.8 887..33e+5 4.89e+6 [R + 5,R + 6 ] Scaled- A Scaled- Scaled- Scaled- Scaled- VaR Scaled- Scaled-
1 1.4.35.3.5..15.1.5 Scaled- -1-8 -6-4 - 4 6 8 1
.8.7.6.5.4.3..1 Scaled- 3 4 5 6 7 8 9 1 3.4.38.36.34.3.3.8.6.4 Scaled-.. -1.5-1 -.5.5 1 1.5 1 Scaled- 3 3
1 3 1 * Scaled- -.,. Scaled- Praez(197) Scaled- Praez 1959 Osborne (M. Osborne, Brownan moon n he sock marke, Operaons Research, 7(1959): 145-173) p y= ln( p / p ) + τ + τ y exp( y / τ ) f( y) = 1 π τ y Praez Osborne g ( ) 1 f y ( ) exp( y / τ ) = π τ y τ y µ f y ( ) exp[ ( y µ ) / ] = 3 π h(y) y ( ) ) hy = f( y ) g( d 4 Raffa Schlafer g ( ) g ( ) v v v/ ( 1) = e v Γ( v /) ( v / 1) 5
E 4 = ) Var( ) = /( v / ) ( g ( ) Raffa Schlafer 4 Scaled- 4 v v/ ( 1) ( v / 1) hy ( ) = e d Γ( v /) v exp[ ( y µ ) / ] v+ π v v v/ ( y µ ) + ( v ) ( 1) exp[ ] = d v+ 3 π Γ( v /) ( y µ ) + ( v ) z = v v v/ ( 1) hy ( ) = [( y µ ) + ( v ) ] exp[ zz ] dz π Γ( v /) ( v+ 1)/ ( v+ 1)/ ( v 1)/ v + 1 Γ( ) ( y µ ) = [1 + ] Γ( v/ )[( v ) π] ( v ) 1/ ( v+ 1)/ 6 1/ h(y) v [ v/ ( v )],y Scaled- Scaled- y Scaled- µ v Scaled- : 1. Gray, B. and D. French 199. Emprcal comparsons of dsrbuonal models for sock ndex reurns Journal of Busness, Fnance & Accounng,17,451-459. Peers, E. (1991).Chaos and Order n he Capal Markes. A New Vew of Cycles,Prces and Marke Volaly. John Wley and Sons. 3. Felpe, A. and Javer, E. (1997).Emprcal dsrbuons of sock reurns 1,Scandnavan Secures Markes199-1995,Carlos III Unversy 4. Per, A.(1994). The Dsrbuon of Sock Reurns: Inernaonal Evdence. Appled Fnancal Economcs,4,431-439 5. Praez P.(197). The dsrbuon of share prce changes. Journal of Busness,45,49-55 6. Campell, Y.,Lo, W. and Macknlay, A (1997). Economercs of Fnancal 4 H. Raffa and R.Schlafer Appled Sascal Decson Theory Harvard Busness School,1961
Markes, Prnceon Press 7. Bennnga S. and Wener Z. (1998), Value-a-RskMahemaca n Educaon and Research,Vol.7 No.4,1-8 8. Press J.(1967), A Compound evens model for secury prces. Journal of Busness,4,317-335 9., 1 7,9-33 1.,14-1 11. 9,9-11 1.,57-58 13. 1 1,1-5 14. 3 9,46-48 15.,, 3, 3,8-33 16. R/S 1 1,1-5 17. 3 1,5-57 18. 19. 1997 Emal: jcdonglc@gscas.ac.cn