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"3MM@ G 7>3A>E39 B>4>@E>9 =EF; 10940;4 >@;>3> 1>;>= 70@4;K= O;300 A@3 CB30B09 1>;>EK3 G 39A3ME 0@3039 N<. %M@M2 A?@M4 M5@M3 CB30B09 1096 10=:=K FM2M@ E389= >@;>3> =L B=89 =89B 70@4;K3 E00E04 E@M;FME39 1>; 10=:=K 0:B82 @M34ME 0;40340;4 >@CC;=0. 9<4 10=:=K EC2L4 E389= M@A4M;89= EO<@0;B09 <><5=B 1>; B=89 0:B82 ?0AA8289= EC30F00=K ; B>E8@>> AAM= 109E BM@ 5 N<. #3 B@;89= AB@0B5389= 54 0:B82 ?0AA8289= EC30F00=K ; B>E8@>> =L  EMBED Equation.3  702A0@B 1CNC 0:B82 ?0AA8289= E389= @G;;B O203406 109300 BM@ <><5=BM4 M=M B@;89= M@A4M; =4@68=. %M4893MM@ "0:B82 ?0AA8289= EC30F00=K ; B>E8@>>" 1E 10=:=K E@=3, ME A2M@89= EC2L4 109403 1>;>E>>@ 1E 10=:CC4 C3 M@A4M;893 @G 109300 EM@M3. =MMA 4M6 E=89 M@A4M;893 <8=8<C<G;0E 0@30 70< =L E389= B2H=893 1>48B>>@ ?@>3=>7G8;6, B=4 7>E8FCC;0= 0:B82, ?0AA8200 C48@40E O240;, <= B=G;M= EC30F00=K B>E8@>>3 E0=30A0= 0:B82 ?0AA8289= C48@4;030 N<. %0<389= 36BM9 =L E389= B2H=89 @G;;B893 ?@>3=>7G;>E O240; 134 =893 1>48B>>@ B>4>@E>9;>E>4 <0H EMF, E0@8= 0:B82 ?0AA82K= EC30F00=K B>E8@>>3 E0=30E =L 70@8< =M3M= >@;>3>>A B0B30;70E04 E@3M4M3 7M@M3 M5@M3 A@3 B0;CC4B09. %C2LA0E (E23G) E3 0H83;06 109300 54 E0<389= A@3 @ 403020@B09 <><5=BCC4 1>; B0B0= B2;@;A= ME A2M@B 8; =4@ E B;E H00@4;030B09 1>;>E, =3 B0;00A ME A2M@MM 109@HCC;A0= 0:B8200A 7>E8E >@;>3>> 1@M= 39FMB 02G G040E39 109E O240; 134 M=M =L A0=E389= HCC4 0;40340;4 E@3M6 109300 EM@M3 N<. =MMA 304=0 E389= M@A4M;893 B>>F>6 7ME4MM 10=:8=4, 0H8339 <=E 589= E389= B2H=MM@ B;1@ E89E EM@M3BM9 EC30F00=K 702A0@K3 B>>F>6 109E =L <0H GCE0; N<. %389= M@A4M;89= C48@4;03K= 0@3CC4 %389= M@A4M;89= C48@4;03K= EM4 EM4M= E0=4;030 109403 10 BM4=89 =M3 =L GAP - H8=68;3MM N<. GAP =L M489= 70A389= 1>38=> EC30F00=4 E389= FM2M@ >@;>3>4 0=E00@0; E0=4CC;A0= 0@30G;0; N<. =4 0:B82 ?0AA82CC4K3 BM4=89 B;1@ E8934ME EC30F00300@ MA2M; 1>;><68B ME=89 40E8= =M;3MM E8934ME EC30F00300@ =L 1;M3;M=M. GAP =L EC30F00=K 702A0@ 1@4 E4 <M4@M<6BM9 0:B82 (RSA) 1>;>= <M4@M<6BM9 ?0AA82K= (RSL) O;300B09 BM=F 109=0.  %23G E 10=:K= FM2M@ >@;>3K3 A3E, 1CC@CC;0E MA2M; B=4 =;;E39 1096 1>;=>. -=M =L 103FK= E4 <M4@M<B389 1BMF <= B=89 GAP-K= EM<6MM=MMA E0<00@=0. %M@M2 A@3 GAP =L E389= <M4@M<6BM9 0:B8200A E389= <M4@M<6BM9 ?0AA82 8E 1093003 E0@CC;=0. %C30F00=K O<0@ =M3M= 702A0@B E389= B2H8= AE4 =89B 40E8= =M;M34M6 1C9 0:B82K= >@;>3>>A 8;3MM@ =89B 40E8= =M;M34M6 1C9 ?0AA82B B;1@ B;E 1>;=>. 9<4 =89B 068;;06 109300 0:B82K= 4C=406 >@;>3> 1>;>= =89B B;1@BM9 ?0AA82K= 4C=406 @B389= E>>@>=4K= A?@M4 1030A06 E389= EM;1M@MM@ >;>E >@;>3> 1CC@=0. %0@8= EC30F00=K O<0@ =M3M= 702A0@B E389= B2H8= 1CC@0E04 ?0AA82 =L 0:B8200A00 8; 1>; A?@M4 =M<M34M6, FM2M@ E389= >@;>3> A=. -5@M3 GAP-B09 B>E8>;4>;4 <=E89= MA@M3 MDD5:B 7;=M. %0@8= BM3 GAP-B09 1>; E389= B2H=89 @G;;B E389= FM2M@ >@;>3>4 =;;E39 1>;>E =L >9;3><6B>9 109=0. GAP-89= 7;M;B4 10=:=K C48@4;0304 BC;30@G 109403 E389= 5@=E89 M@A4M;893 E0@CC;403 134 M=M =L 40@00E EM;1M@BM9 109=0:  =4:  EMBED Equation.3 - %;MM34M6 1C9 E389= FM2M@ >@;>3K= @G;;B; GAP - %389= <M4@M<6BM9 0:B82 ?0AA82K= O;300;  EMBED Equation.3 - %;MM34M6 1C9 1>38=> EC30F00=K E389= B2H=89 @G;;B; -FA89= 1;M3B 43=M6 EM;MEM4 EM@M2 E389= B2H8= AE4 M5@M3 GAP FM2M@ E389= >@;>3K3 A3=. %0@8= E389= B2H8= 1CC@0E04 A@3 GAP FM2M@ E389= >@;>3K3 A3=. %M@M2 E389= B2H=89 @G;;B ?@>3=>7G8;A>= G83;M;4 1>;>= EM<6MM3MM@ O203420; 10=:=K 1>48B FM2M@ E389= >@;>3K= A;B B;2;A= EM<6MM=4MM 109=0. 9<4 GAP -89= EM<6MM =L BCE09= 10=:=K E;MM6 109300 M@A4M;89= B2H8=3 E0@CC;=0 3M6 B>>F>6 1>;=>. %M@M2 10=: GAP-aap 40<;0= >@;>3> EF;4E39 3MAM= AB@0B53893 10@820; GAP - 893 BM3 109;306 E389= M@A4M;893 1CC@CC;=0. -=M B>E8>;4>;4 E389= B2H=89 @G8;;BA ; E0<00@0= 10=:=K FM2M@ E389= >@;>3> B>3B<>; 109=0. 3 B0;00@ 10=: 8@MM49= E389= B2H=89 @G;;BA >@;>3> >;>E 7>@8;3>B>9 GAP -893 84M2EBM9 C48@4403 1096 1>;>E N<. 9< CG@00A GAP 0=0;8789= 8;M@E89;M;893 0H83;0= E389= M@A4M;893 C48@40E GCE0; 0@30 1>;>E =L E0@03406 109=0. = C48@4;03K3 E389= 1>4;>3>4 1>48B =4MA;M;893 =L >;3>6, A@3 E389= <0@689= B0;00@ A0=CC;30 4>E8> 3E GCE0; 0G E>;1>34>;B>9. 0=09 >@=K EC2L4 C3 0@30G;0;K3 0H83;0E04 B>4>@E>9 E=4@M;4 109403 =L: 1. >48B 0<L4@0; 4MM@ 0:B82K= 79; 0=38C4K= >@;>3>B 10940; 1>;>= 45?>78BK= B;1@ BM@ 1@ =M3M= 7M@M3 ?@>?>@F8>=0;80@ @G;344 10940339, E23G EBM9 0:B82 1>;>= ?0AA82K= 1>48B E389= B2H8=3 B>4>@E>9;>E ACC@L =L E0@8;F0= @ 109403 7M@M3 E=4@M;4 >@H4>3. "89< CG@00A GAP-89= 0H83;0;BK= @ 36893 4MMH;;ME89= BC;4 B=893 EC30F00=K E0@LF0=3C9 1>38=> 702A0@B EM@M3;ME =L 8; 0G E>;1>34>;B>9 134 E23G EBM9 7MM;;M34893 B=89 E389= @G;;B89= <M4@M<689= 7M@M3;M;MM@ =L 1;M3;M= 02G 7ME =L @ 4=BM9. =3MEM4 7MM;;M3489= E23G E389= ACC@L =L E0@8;F0= O;300B09 109403 =L ACC@L E389= @G;;B89= 5 1>;>= 40;09FK3 =0@89= B>4>@E>9;>E 0ACC4;K3 8EMMEM= E=4@M;BM9 1>;3>=>. 2. %389= ?@>3=>7G;>;K= 0ACC4;K3 H8942M@;MAM= 3M6 7AM= B>E8>;4>;4 GAP-893 CO= E0B0= C48@40E 0ACC40; 4MM@ @ =M3M= E=4@M; 109403 =L 10=: 1>;>= E0@8;F03G89= EAM; A>=8@E;K= 7@G8;4= N<. 8HMM;1M; EM@M2 10=: E389= B2H=89 A;B893 E;MM6 109E04, >;3>E 7MM;893 72E= E23G E3MM@ >;3>EK3 EA=M. %0@8= 7MM;4M3G E389= A;B893 <M4M@G 109300 3M2M; BM@ 7MM;893 72E= =M@;MAM= E3MM@ 020EK3 7>@8=>. 0@CC=K 10=:CC4K= 9; 068;;0300=4 E389= M@A4M;89= C48@4;03K= BC@H;0304 GAP-0=0;8700A 304=0 SPREAD 3M6 =M@;M344M3 0@30 1CNC FM2M@ E389= <0@689= 0@30 @3= =M2BM@AM= 109403.  0=:=K FM2M@ E389= >@;>3>4: E389= =>@<K= @G;;B, 10=:=K >@;>3K= =>@<, =89B >@;>3> 70@;03K= EM<6MM 7M@M3 =;;; 7;=M. %23G E 10=:=K >@;>3K3 A3E, 1CC@CC;0E, MA2M; @G8;4339 1096 1>;=>. -43MM@ @G;;B4: MM;89= 103FK= 1BMF; :B82 ?0AA82K= E389= B2H=89 @G;;B89= <M4@M<6; GAP-89= EM<6MM 7M@3MMA E0<00@=0. 2.4.2. =89= M@A4M;: -=M M@A4M; =L 1CA04 M@A4M;MMA 8EMMEM= E0<00@00;B09 134 BCE09= 1093CC;;03K= @59BM=3MMA E0<00@004 8EMMEM= <M4@M<6 =4@BM9 M@A4M;89= =M3 N<. 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VAR (Value at Risk) . . . . VAR (Value at Risk) . VAR 㺺 Delta normal VAR, Historical Simulation VAR Monte Carlo Simulation VAR- . 1. Delta Normal VAR Delta Normal . 㺺 (-1.1). (95% 99%) .  EMBED Equation.3  (3.1) :  EMBED Equation.3  - .  EMBED Equation.3  - . Delta normal 뿿 o .  EMBED Equation.3  뺺 . 뺺 VAR . EWMA GARCH 뿿  EMBED Equation.3 - 뿿 .  SHAPE \* MERGEFORMAT  GARCH GARCH (Generalized autoregressive conditional heteroskedastic) 㺺 1982 , 1986 濿 .  EMBED Equation.3   EMBED Equation.3  ,  EMBED Equation.3  .  EMBED Equation.3  (3.2)  EMBED Equation.3  . GARCH-  EMBED Equation.3 - 濿 .  EMBED Equation.3 - . GARCH .  EMBED Equation.3 -  EMBED Equation.3   EMBED Equation.3  . GARCH(1,1) .  EMBED Equation.3  (3.3) :  EMBED Equation.3 - ,  EMBED Equation.3 - ,  EMBED Equation.3   EMBED Equation.3  . ARCH(1) 㺺  EMBED Equation.3  (Generalized) . EWMA GARCH EWMA (Exponentially weighted moving average) .  EMBED Equation.3  忿  EMBED Equation.3 - ,  EMBED Equation.3 - .  EMBED Equation.3  (3.4) GARCH . GARCH  EMBED Equation.3  㺺 . JPMotgen-  EMBED Equation.3  . 2. Historical Simulation VAR- 人 delta normal . VAR .  SHAPE \* MERGEFORMAT  3. Monte Carlo Simulation VAR- 人 Historical Simulation Monte Carla . Monte Carla . : ҿ . 뿿  EMBED Equation.3  . . ҿ . . ҿ . II. GBM GBM (Geometric Brownian Motion) 人 Markow 㺺 Markow efficient market . . Wiener  EMBED Equation.3  - 㺺  EMBED Equation.3   EMBED Equation.3 - 㺺  EMBED Equation.3 - .  EMBED Equation.3  (3.5)  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  . ̺  EMBED Equation.3 - . Generalized wiener  EMBED Equation.3  wiener 㺺  EMBED Equation.3   EMBED Equation.3  .  EMBED Equation.3  (3.6) (stochastic)  EMBED Equation.3  .  EMBED Equation.3  (3.7) Ito Generalized Wiener 㺺 .  EMBED Equation.3  (3.8) GBM GBM  EMBED Equation.3 -뺺 . VAR (Value at Risk) . GBM . GBM ito 㺺 .  EMBED Equation.3  (3.9) :  EMBED Equation.3  - ,  EMBED Equation.3   EMBED Equation.3  - .  EMBED Equation.3  - .  EMBED Equation.3  (3.10)  EMBED Equation.3 -  EMBED Equation.3   EMBED Equation.3  . GBM 人 㺺 . (3.9)  EMBED Equation.3  -  EMBED Equation.3  - .  EMBED Equation.3  (3.11) :  EMBED Equation.3  -  EMBED Equation.3  㺺 (3.11)- :  EMBED Equation.3  (3.12) : . 95%- 97.5% (=NORMSINV{0.975}=1.96). 1.3.2. OPTION , 㺺 option- . Option- 뿿 2 . option- 뿿 . option- 뿿 . option . Option- (Call option, Put option) 뺺 . 뺺 . Call option- .  EMBED Equation.3  (3.1)  EMBED Equation.3  ( ),  EMBED Equation.3  . Put option- .  EMBED Equation.3  (3.2) Option- in the money, at the money, out of the money , .  EMBED Equation.3  call option- ,  EMBED Equation.3  put option- .  SHAPE \* MERGEFORMAT  SHAPE \* MERGEFORMAT   SHAPE \* MERGEFORMAT  3.3- Call option call- . option- . option . ͺ㺺 . Option- option- Black-Scholes option- . Black & Scholes BS Fischer Black Myron Scholes 1972 option- 1997 . . Robert C.Merton 1997 . . 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C48@4;0304 M@A4M;893 EO=0E C48@40E04 7>@8C;034A0= 2. 0@8;600=K 0;10=4 7>@8C;034A0= <M4MM;M; 109E QAB>9 134 C3 <M4MM;;89= 1BMF =L 7>@8C;0;B00@ 1;M3;M34AM= 0H83;0;BK= H00@4;0304 =89FAM= 109E QAB>9. %M4893MM@ M@A4M;89= C48@4;030, ?@0:B8: <5=56<5=B89= 1@M;4ME= EMAM3 G 30@30A0= H8942M@89= EO=0;B, 40E8= EO=0;BK3 H00@406 109403 B>3B>;F>> N<. -@A4M;89= C48@4;03K= GCE0; M;5<5=B4: 0=:=K 0@8;600=K 1>4;>3>, M@A4M;89= C48@4;030, E4;<@89= ?@>F5AA89= 7>E8>= 1093CC;0;B, 0H83;0E =M@ B><LQ>-B5@<8=>;>389= 0ACC4;CC400@ <0H =0@89= =O3B 1>;>2A@CC;A0=, 10@8<B6CC;A0= 70@G8<, 6C@0<; @8;600=K 3070@ EM;BAMMA ; E0<00@0;B09 185 400A0= M@A4M;89= C48@4;03K= 103 1093CC;0E; 0E 7MM;89= 1>;>= 7MM;89= M@A4M;89= ;8<8B893 B>3B>>6, B=89 E0=30;B04 EO=0;B B028E, B=G;M= A0;10@ =M36, 1A =CB03, M489= 70A389= A0;10@, 10=:=K 1BMM34ME= 9;G8;3MM 1@89= C48@4;03K= 6C@0< 7;M;B893 B>3B>>E; #48@4;0304 E@3ME M@A4M;89= B0;00@E <M4MM;;89= 402B0<6 / >; B;2 B=89 402B0<6 4@ 1@ 109403, O;0=3CO0 70E 7MM;89= M@A4M;89= B0;00@E <M4MM;;4 /; -@A4M;89= C48@4;03K= 1>;>= EO=0;BK= 1E M;5<5=B4 B>3B<>; 0C48B>@>>@ EO=03406 109E QAB>9; -@A4M;89= C48@4;03K= =4AM= M;5<5=B4 =L: 1. 8<8B B>3B>>E; 0=:=K C48@4;030 1>;>2A@CC;A0= AB@0B5389= 403CC E;MMEM4 1M;M= 109300 M@A4M;89= 72H@34E EO7300@ EM<6MM3 B>3B>>E>4 >@H8=>. -43MM@ ;8<8B893 10=:=K 4>B>>4 6C@0<, 70020@, 0@30G;0;CC400@ B>3B>>6 3=. 2. -@A4M;893 B>3B>>E 10 B2H8=3 B>4>@E>9;>E. -@A4M; >@H86 109=0 3M4M3 1>; B=89 O<0@ =M3M= @=;89= 70320@ 109E 10 E0@8= B=89 0;LB5@=0B82 EC28;10@ 1>;>E @=;89= @ 70< @3M;6 03CC;03406 10943893 EM;ME EM@M3BM9 109=0. @=;89= 70320@K= H8=68;3MM 1>; M@A4M;893 =M;ME, B=893 C48@40E04 <0H GCE0; EM@M3AM; 1>;4>3. #3 H8=68;3MM =L 10=: C3 B@;89= M@A4M;4 @B6 109300 EC30F00=K =M;3MM, M@A4M;89= =;;;89= 7M@M3;M; - 0H83 0;4034;K= B>>= 7;M;BMM@, <= B=G;M= B00;0<6B09 1>;>= B00;0<639 =EF; 1094;K= <0304;0;K= =M;3MM 7M@M3B =4MA;M344M3. -@A4M;89= B@;4#48@4;03K= 0@30G;0;, E0=4;030, B5E=8:!0=E389= 10 7>E8>= 1093CC;0;BK= EM@M3AM;E B@;89= A0=E389= M@A4M;4(8=68;3MM; EO=0;B; <>=8B>@8=3; ;8<8B B>3B>>E; 4>B>>4 EO=0;B; C48@4;03K= <M4MM;;89= A8AB5<.8<8B, B09;0=, 6C@0<, AB0=40@B, 70020@,B>3B>>;MM;89= M@A4M;MM;89= 103FK= C48@4;030; M;M34;M;B; 825@A8D8:0F8, E5468@;ME, 10B0;300, 10B;0= 400;B, 0=38;0;,"#%!0=, 7MM;89= 0=38;0;%@2E G0420@K= M@A4M;#48@4;030, 10;0=AK= C48@4;030, <=3= E@=389= E4;;89= C48@4;030, =5F89= C48@4;030, 0:B82K= 103FK= C48@4;030=E403G 10 E>Q@4>3G =F; <5=3=89 70E 7MM;89= EM@M3A;4%389= M@A4M;#48@4;030;  ; E5468@;ME; =M B>3B>>E.%389= DLNG5@A4; >?F8>=CC4; A2>?CC4.0;NBK= M@A4M;MM;BBM9 ?>78F89= C48@4;030; E5468@;ME; 4825@A8D8:0F8.0;NBK= DLNG5@A4; >?F8>=CC4; A2>?CC4; <5=35=89 70E 7MM;89= EM@M3A;4.0=:=K EM@M36;6 1C9 0;L =M3M= 9; 068;;0300, 9; 068;;0300=K G83;M;, A0;10@ =M36 1@89= 1>;>= =89B 10=:=K EM<6MM3MM@E M@A4M;89= 72H@34E B2H=89 B>>= 7;M;B893 B>4>@E>9;>E =L <0@:5B8=389= AC40;300B09 =O3B E>;1>>B>9 <0H GCE0; 0@30 EM<6MM N<. -@A4M;893 B>4>@E>9;>E A8AB5< 3C@20= =4AM= 1@4;M3GMMA B>3B4>3: ;4034;K= EM<6MM; @3M;6;ME EC30F00; -@A4M;89= <0304;0;; 3. -@A4M;89= C48@4;03K= B>3B>;F>>, EO=0;B -@A4M;89= C48@4;03K= B>3B>;F>>=K EM@M368;B =L, AB@0B5389= C48@4;030, 7>E8>= 1093CC;0;BK= =M36489= B2H8=4 MA2M; O<0@ =M3M= =0@89= 9; 068;;03003 EM@M36;MEM4 1E =M36489= E0@8;F0= 9; 068;;0300300@ EM@M368=M. -@A4M;89= EO=0;B -@A4M;89= EO=0;BK= DC=:F =L 10=:=K 39FMB3M3G 068;B=K @M3B 068; 109E00A 304=0 O=7 1@89= B2H=89 C48@4;03K= 1>;>>4 A3M= 1093CC;03G84, EC2L =89;;M3G489= EO=0;B0=4 109E QAB>9 N<. -@A4M;89= 72 >=>2GB>9 EO=0;B 109EK= BC;4: -@E <M4;89= 72 EC200@8;0;B; ;10= BCH00;K= 70020@G8;300; "3A 1>;>2A@>=3C9 <M4MM;M; 40<6CC;0E AC203; 0=:=K 9; 068;;0300 1>;3>=4 M@A4M;893 72 B>4>@E>9;>EK= BC;4 >;>= B0;00A =L, O=7 1@89= 109@ ACC@8=00A E0=40E H00@4;030B09 10 0;L =M3M= 9; 068;;0300=K M@A4M;893 B>4>@E>9;>E>4 =M36 1@ B>4>@E>9 EM<6MM=89 GCE0; <M4MM;;893 03CC;403 1096 1>;>E N<. 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" >=8B>@8=3" 3M4M3 =L 109=3K= 185 400A0= M@A4M;89= EO=0;B, =M;3MM=89 A8AB5< N<. -=M =L <M4MM;;89= 1>;>= @M3 E0@8CF03G89= B09;0=, 4>B>>4 10 304004 0C48B, <= B=G;M= 7MM;89= H8=68;3MM <MB89= H8=68;3MM =M;3MM=89 9;4;MM@ EM@M368=M. >=8B>@8=3>>@E B09;0= =L <5=565@4893 9; 068;;0300=K 45B0;LG8;A0= 4M;3M@M=39 <M4MM;;MM@ E0=30E 134 C3 <M4MM;;4 =L 9; 068;;0300=K C@A30; 1094;K= B0;00@ 4= H8=68;3MM E896, 0;L =M3M= B@;@ 1>;>= =89B A8AB5<89= EC2L4 EM@M36;ME H8942M@ 30@30E04 GCE0; 0G E>;1>34>;B>9. -@A4M;89= C48@4;03K= MFA89= 7>@8;3> =L 10=:=K 0H83, FM2M@ E389= >@;>3>, @89= E@=3=4 A@3@ =;;E 0;8200 =EF; 1094;00A 709;AE89E @ 403020@K3 =L 1CC@CC;0E, 10=:=K EM289= 068;;0300, 0NC;39 10940;K3 E0=30E04 >@H8=>. 2.3. 0?8B@>= 10=:=K 20;NBK= E0=H=K ( 2@> ) M@A4M;893 C48@40E 70@8< 0ACC40; VAR 0@3K3 EM@M3;ME =L VaR / value at risk / =L A0=E389= 1BMM34ME=89 103F00A B>4>@E>9 EC30F00=4 B>4>@E>9 <0304;0;K= B2H8=4 E;MM6 1>;>E 0;4034;K= 4MM4 EM<6MM3 8;M@E89;4M3. VaR - 3 M@A4M;89= AB0=40@B 0@30 1>;3>EK3 72E= A0=E389= 7>E8>= 1093CC;034A0= B><>>E>= EC40;400=K 9; 068;;0300=4 1CA, 10=:, 400B30;K= :><?0=8 E@=3 >@CC;0;BK= 8=AB8BCB, A0=E389= 1CA 1093CC;;03CC4 G 3MAM= EM@M3;ME893 72;6 109=0. =893 1E A0=E389= EM@M3;M3G4M4, >;>= C;AK= :;8@8=389= B2, 0<5@8:89= E>;1>>=K =F89= 10=: 10 =MB F00A 0@8;600=K E>@>> 7M@M3 =L 4M<686 72;6 109=0. 1993 >=K 7-@ A0@4 "CG" 3@C??K= 8;B3M;4 0=E >;>= =89BM4 VaR B0=8;FCC;034A0=00A E>9H VaR-= EM@M3;MM, EM@M3;M3G89= B>> AA@ 109=0. =>;K= EC2L4 0@ =L M@A4M;89= 0@30 3M43893 >@8>= /1997/, >24 /1998/, !0C=4M@A /1999/ =0@ 30@30A0= 10 BM4 4@M< 10 A>=3>;BK3 AB0=40@B 4MM@ =4MA;MAM=. 0=09 >@=K EC2L4 M=M 0@30 =L B489;= 4M;3M@MM39 134 >=3>;10=:=00A M=M 0@300@ E0=H89= M@A4M;MMA AM@389;ME893 72;43 134 M=M 0@300@ B>>F>EK= BC;4 =M<M;B 72H@; 02403. 0@00E H0;3CC@K3 E0=30A0= 10=:8=4 72H@; >;3>4>3. 0=: =L M@A4M;89= C48@4;03K= 0ACC4;K3 E0@8CFA0= BCA309 =M36BM9, M=ME =M36 =L BCA309 <0B5<0B8: 70320@ 1>;>= ?@>3@0< E0=30<689= 403CC 10=:=K 70E 7MM;MMA E;MM6 1>;7>H39 0;4034;K= B>>F>>3 4@ BCB0< 30@306 C48@4;0304 B0=8;FCC;403 B>3B>;F>>3 189 1>;3>=>. -@A4M;89= C48@4;03K= 0ACC4;K3 E0@8CFA0= =M3689= C48@4;030 =L BCE09= M@A4M; 1E89 0:B82 ?0AA82 E@=3893 70E8@0= 70@FCC;0E M@EBM9 109E 134 BCA309 70320@ 1>;>= 4@>3@0< E0=30<689= BCA;0<6B09300@ B>>FA>=. -@A4M;89= =M;3MM3 0@8;600=K ;8<8B B>3B>>E 9; 068;;0300=400 0H83;0403. 0=:=K M@A4M;89= C48@4;03K= B0;00@, O;0=3CO0 068;B=CC4K= M@E @M3 E;MME E0@8CF;03K3 BCA30A0= BCA309 4@M< 6C@0<, 70020@, 72;<6893 10B;0E 7M@M3 1>;>= ?@>3@0< E0=30<689= B0; 4MM@ H00@4;030 B02L403. @>3@0< E0=30<684 B02L403 H00@4;0300A 68HMM B0B20;: VaR - 3 4@ BCB0< B>>F>E G0420@B09 109E ;40340; E;MME <0304;0; =L 99 EC2LB09 109E, =4 EM289= B0@E0;BB09 A0=0<A0@39 EM<6834ME=89 =O3BK= DC=:FK3 0H83;0403 %>;1>34>E <M4MM;;89= 1007K3 3 A0@4 4>@ E0O6 =M3 C400 H8=MG8;6 109E QAB>9 3ME <MBG8;M= 109403. >=3>;10=:=00A A0=0; 1>;3>A>= B><JQ>;>; 40@00E 10940;B09 109=0. VaR 0@300@ 20;NBK= E0=H89= BM3H8B3M;89= 0;4034;K3 B>>F>E =L 04004 20;NBK= E0=H89= BM3H8B3M;MMA E;MME 0;4034;K3 VaR 0@300@ B>>F>E4>> AB0=40@B DC=:F 1E89 70320@K3 0H83;06 1>;=>. -=ME 0@3K3 B><JQ>3>>@ 8;M@E89;1M; 40@00E 10940;B09 109=0:  EMBED Equation.3   EMBED Equation.3  & & & & & & & & & & & & & & & & .  EMBED Equation.3  =4  EMBED Equation.3  =L BCE09= 304004 20;NBK= ?>78F>>A E;MM6 1>;7>H39 0;40340;,  EMBED Equation.3  =L 304004 20;NBK= 0:B82 ?0AA82K= ;4M34M;,  EMBED Equation.3  =L  EMBED Equation.3  0G E>;1>34;K= B2H8= 1E89 EM289= B0@E0;BB09 A0=0<A0@39 EM<6834ME=89 =O3BK= DC=:FK= 8=25@A8,  EMBED Equation.3  =L BCE09= 304004 20;NBK= E0=H89= AB0=40@B E0709;B,  EMBED Equation.3  =L BCE09= 304004 20;NBK= E0=H89= 0@8D<5B8: 4C=406 N<. 04004 20;NBK= 103F00A E;MM6 1>;7>H39 0;4034;K3 B>>F>E4>> 40@00E B><JQ>3 0H83;0E 134 0G E>;1>34;K= B2H8=3 1 EC280@ B>>F>6, 304004 20;NB BCA 1@89= E0=H89= E0<00@;K3 E0@30;70= 7=M.  EMBED Equation.3  !B0=40@B E0709;BK3 B>>F>E4>>  EMBED Equation.3  ><JQ>3>>@ B>>F=>. VaR - B>>F>E 0@3K3 68HMM3MM@ E0@CC;10;:  10=: 5 A0O 4>;;0@K= ?>78F8 =MMAM= 3M6 72M; =89B 304004 20;NBK= 103F00A E;MME 0;4034;K3 B>4>@E>9;>E>4: MM;BBM9 ?>78F893 B3@3@ 8;M@E89;=M. "3@389= 0< 4>;;0@B09 E0@LF0E E0=H 1164 109300 1>; BCE09= =MM;BBM9 ?>78F89= 4= 5,820.0 A0O B3@3 1>;=>. 04004 20;NBK= AB0=40@B E0709;BK3 B>>F=>. 0=09 68HMM= 4MM@ B3@3 0< 4>;;0@K= AB0=40@B E0709;B 15 EC2L 109=0 3M6 7L5. %;MM6 1>;7>H39 0;4034;K= 4MM4 EM<6MM3 B>4>@E>9;>E. =4 0;40340; E;MME <0304;0; =L 99 EC2L 109E04 EM289= B0@E0;BB09 =O3BK= DC=:FK= 8=25@A8 >9@>;F>>3>>@ 2.326 109=0. VaR=5820.0*(2.326*15%)=2030.59 A0O B3@3 1CNC 1,7 A0O 0< 4>;;0@ 1>;=>. -=ME 0@3K3 40@00E 1094;00@ =M;3MM3 A096@CC;0= 10=:=K 9; 068;;0300=4 0H83;0E 1>;><6B>9. =3ME89= BC;4 40@00E 79;A893 <M4ME H00@4;030B09. %C30F00=K FC200, B=89 1@M;4ME= EMAM3. !>=3>= 02A0= 7;M;B89= F03 EC30F00=K 4MA 40@00;A0= =M364M4 E0@30;70E CB3CC400A B>3B>E >;>=;>3893 EC30F00=K FC200 3M4M3. %C30F00=K FC200 =L 68;, cap, C;8@0;, cap, 4@, F03, <8=CB, A5:C=4 3ME <MB EC30F00=K =M364M4 E0@30;70= 33443. %C30F00=K FC200 =L 40@00E 1@M;4ME= EMA34MMA B>3B4>3. =4: > "@5=4 1CNC G83 E0=4;030 - ( TR-Trend) > #;8@0; MA2M; A0@K= =;;;-( S-Seasonality ) > &8:; 1CNC <G;3 =;;;-( C-Cycle ) > (>: 1CNC A0=0<A0@39 EG8= 79;89= =;;;-( I-Irregular activity or Shock) "@5=4. 2G 7M6 109300 EC30F00=K 702A0@B BCE09= FC200=K B2H=89 CB30 =M3 1>; AE MA2M; 1CC@0E G83;M;BM9 10920; E0@30;7CC;0= AE MA2M; 1CC@0E B@5=4BM9 EC30F00=K FC200 3M=M. "CE09;10;, E= 0<K= B>>=K A;B, H8=6;ME CE00=, B5E=8:89= 4M2H;89= =;3@ C;A >@=CC4K= 1>48B 4>B>>4K= =89B 1BMM34ME= AE E0=4;030B09 109403 1>; =E= AM@3MM34ME39 10930;89= 10O;389= EM<6MM 68;MMA 68;4 O<0@ =M3 EM<6MM3MM@ 1CC@403. "@5=4893 =89;<M; EC30F00=K FC200=K EC2L4 7M@3M;4MM EM4, EM4M= CB3K3 4C=406;0E 0@300@ B>4>@E>9;6 1>;=>. #;8@0;, A0@K= =;;;. #;8@0; MA2M; A0@00@ 334A= EC30F00=K FC200=K EC2L4 BCE09= C;8@0;, A0@K= H8=6 G0=0@ 68; 1@ 402B03406 10920; B=893 C;8@0; MA2M; A0@K= =;;;BM9 109=0 3M4M3. #;8@0;, A0@K= =;;;893 C;8@;K= 8=45:AMM@ B>4>@E>9;4>3. #;8@0;, A0@K= =;;; =L EC30F00=K FC200=K 68;89= 4>B>@E <G;3 EM;1M;7;893 E0@CC;0E 10 M489= 70A389= A0;10@K= >=F;>3, 06 0EC9= EM2 H8=6, 1BMM34ME=89 H8=6 G0=0@00A E0<00@403. 0=09 >@=K EC2L4 68;89= 4@2= C;8@0;B09300A H0;B300;0= 8EM=E 1BMM34ME=89 9;42M@;M; C;8@0;, A0@K= =;;;BM9 109403. G;3 =;;;. %C30F00=K FC200=K B>4>@E>9 54 E0@30;706 109A0= =EF; 10940; C@B EC30F00=4 40E8= 402B0340E H8=6BM9 10920; B=893 <G;3 =;;;BM9 3M=M. -=ME <G;3 =;;; =L @89=E =3@A= 589= EC30F00=K E>68<4;>>@ B09;10@;034403 02B>@53@5AA82 ?@>F5AA AR(autoregressive process) 109403. 2B>@53@5AA82 ?@>F5AA89= EC2L4 E0<389= GCE0; >9;3>;B =L AB0F8>=0@L 109E 0ACC40; N<. %C30F00=K FC200=K CB3CC4K3 B>4>@E>9 EC30F00300@ H8;6;A=89 40@00 4C=406, 48A?5@A, :>20@80FCC4 =L BM=F 109403 FC2003 ABAI8>=0@J FC200 3M=M. G;3 =;;; =L BCE09= 7;M;BM4 O<0@ =M3 304004 5G8;AM= =; BCAA0= 1094;K3 8;B3M4M3. -=M =;;;89= 5 =L 68;MMA 4MMH EC30F00B09 109=0. 0:@> M489= 70A03B 1>48B 4>B>>4K= =89B 1BMM34ME= 89< =;;;BM9 10943893 184 <M4=M. !0=0<A0@39 EG8= 79;89= 1CNC H>:K= =;. %C30F00=K FC200=K CB30 =L 304004 3M=MB89= =;;;89= C;<00A A;B, 1CC@0;BK= E0=4;0300 B@ EC30F00=4 0;40E 7M34;893 A0=0<A0@39 EG8= 79;89= 1CNC H>:K= =; 3M4M3. (>: =L @ 0A0@ 8E <M4MM;;893 03CC;403 134 BM@E <M4MM;;893 B>>F>E 4=MMA MA(moving average) ?@>F5AA>>@ 70320@G8;403. %C30F00=K FC200=K 4@2= 1@M;4ME= EMAM3 =L =89;1M@ 10 @62M@ 3MAM= E>Q@ =4AM= 1BMFBM9 109403. =4: 89;1M@ 6ym3if=TR+S+C+I @62M@ 6ym3if=TR*S*C*I -43MM@ 1@M;4ME= EMA3893 Eviews ?@>3@0< E0=30<689= BCA;0<6B09300@ <0H A09= =M;3MM E896 1>;=>. 8HMM =L B@5=4893 EM;1M@89=E =L EC2L4:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  1>;4>3 134 M43MM@893 Eviews ?@>3@0<00@ =M;6 1>;=>. =3MM4 2@>389= E0=H893 Eviews 4 ?@>3@0<<K= BCA;0<6B09300@ H8=68;6 VaR-K= 70320@ 30@30. 1. 1986 >=K 5 A0@00A 2007 >=K 5 A0@K= 1-=893 E@BM;E 52@>389= E0=H 1CNC EC30F00=K FC2003 0H83;0O. -=M =L H8=68;3MM E89EM4 E0=30;BB09 <M4MM;M; N<. %C30F00=K FC200300@ 1093CC;A0= 3@0D8:  2. "@5=4893 =M;L5. . 204@0B;03 B@5=4 3M6 72M; M=ME =M;3MM =L 0G E>;1>34>;B>9 EM489 G 7;M;B4 <CC 30@A0= 109=0. Dependent Variable: EUROMethod: least SquaresDate: 05/14/07 Time: 19:53Sample(adjusted): 05/20/1986 15/01/2007Included observations: 5466 after adjusting endpointsVariableCoefficientStd. Errorz-StatisticProb.C1.2063320.005537217.87440.0000T-3.44E-054.59E-06-7.4921310.0000T^23.95E-098.00E-104.9308860.0000R-squared0.027215 Mean dependent var1.150760Adjusted R-squared0.026852 S.D. dependent var0.127276S.E. of regression0.125556 Akaike info criterion1.311577Sum squared resid84.46463 Schwarz criterion1.307891Log likelihood3518.681 F-statistic74.64631Durbin-Watson stat0.003403 Prob(F-statistic)0.000000 . 9<4 M=ME B@5=4893 402E0@ ;>30@8D< 1>;>= 38?5@>1>;;>3 3ME 7M@3MM@ =M;3MM3 A096@CC;0= <= AR- 3 =M;MEM4 70320@ =M;MM= A0968@A0= E0@03406 109=0. Dependent Variable: EUROMethod: least SquaresDate: 05/14/07 Time: 20:55Sample(adjusted): 05/20/1986 15/01/2007Included observations: 5466 after adjusting endpointsConvergence achieved after 9 iterationsVariableCoefficientStd. Errorz-StatisticProb.C-26.5275711.95588-2.2187890.0265T0.0030690.001132-2.7120360.0067T^22.52E-078.57E-082.9432750.0033LOG(T)4.3062011.8147312.3729140.01771/T302.4044126.34952.3933950.0167AR(1)0.9974350.0003103222.1910.0000R-squared0.996698 Mean dependent var1.150791Adjusted R-squared0.996695 S.D. dependent var0.127268S.E. of regression0.007316 Akaike info criterion-6.996257Sum squared resid0.286604 Schwarz criterion-6.988884Log likelihood18755.97 F-statistic323228.6Durbin-Watson stat2.024610 Prob(F-statistic)0.000000Inverted AR Roots1.003. =89 40@00 ARCH / autoregressive conditional heteroskedasticity / 1>;>= GARCH 3MAM= 70320@00@ =M;6 20@80F893 30@306 02=0.  EMBED Equation.3  0@306 02A0= M:=><5B@8:A89= 4@<89= 403CC 20@80F00A O73CC@ 30@30E N< 1>; AB0=40@B E0709;B 30@0E 1>;=>.  EMBED Equation.3  -=ME AB0=40@B E0709;BK3 E>Q@>>@ @686 =M<6 E0A20; 95 EC289= <0304;0;K= B2H8=4 1>4>34A>= Var, 3C@200@ @686 =M<6 E0A20; 99 EC289= <0304;0;K= B2H8=4 1>4>34A>= VaR-= 70320@ 30@G 8@ME 1>;=>. =3MM4 Eviews ?@>3@0<<K= BCA;0<6B09300@ 4MM@E 1>4>;BK3 E89AM= @ 4=3 E0@20;: Estimation Command: ARCH EURO C T T^2 LOG(T) 1/T AR(1) @ Estimation Equation: EURO = C(1)+C(2)*T+C(3)*(T^2)+C(4)*LOG(T)+C(5)*[AR(1)=C(6)] Substituted Coefficients: EURO = -11.98119732 - 0.001713214601" + 1.512346482-07*("^2) + +2.102372787*LOG(T) + 157.4637276*(1/") + [AR(1)=0.9970263182] Dependent Variable: EUROMethod: ML-ARCH (Marquardt)Date: 05/16/07 Time: 20:55Sample(adjusted): 05/20/1986 15/01/2007Included observations: 5466 after adjusting endpointsConvergence achieved after 39 iterationsVariance backcast: ONVariableCoefficientStd. Errorz-StatisticProb.C-11.981207.250006-1.6525780.0384T-0.0017130.000742-2.3098920.0209T^21.51E-075.90E-082.5642990.0103LOG(T)2.1023731.1158431.8841120.05951/T157.463770.014142.2490280.0245AR(1)0.9970260.0006101633.4580.0000Variance EquationC ARCH(1) GARCH(1)9.31E-07 0.040501 0.9424011.65E-07 0.003730 0.0056235.627073 10.856678 167.60460.0000 0.0000 0.0000R-squared0.996697 Mean dependent var1.150791Adjusted R-squared0.996692 S.D. dependent var0.127268S.E. of regression0.007320 Akaike info criterion-7.077489Sum squared resid0.286719 Schwarz criterion-7.066429Log likelihood18976.67 F-statistic201823.6Durbin-Watson stat2.022972 Prob(F-statistic)0.000000Inverted AR Roots1.00  >48B 10 B>>F>>;A>= CB30 ;4M34;89= 3@0D8:893 =M3B3M6 E0@20;:  2007 >=K 12 A0@K= 31 4@893 4CCAB0; E0=H893 B00<03;020; 40@00E 4@ 7C@03 E0@03406 109=0.  "00<03;0;K= 3@0D8:00A E0@0E04 2@>389= E0=H 2007 >=K 12 A0@K= 31 4@893 4CCAB0; B>3B<>; A;BBM9 109E00@ E0@03406 109=0. -=ME 70320@K3 0H83;0A0=00@ 8@MM494 2@>389= E0=H O<0@ 10940;B09 109EK3 C@L4G8;0= <M4M6 BCE09= 10=:, A0=E389= 1093CC;;030 =L 2@>389= E0=H89= M@A4M;MMA 1@M= AM@389;6 G040E 1>;><6B>9 1>;6 109300 N<. 3=M;B 0E 7MM;89= @A;4=B =389= =893M<4 M@A4M;893 AC4;0E393MM@ 187=5A89= 0H83 >@;>3>> =M<M34;6 E;MM6 1>;7>H39 0;4034;00A @893 AM@389;6 G04=0 3M4M3 =L 8EMMEM= 3M=M= >9;3>;B 134 109E G 1>;><639 79; N<. %M@M2 109;00 3MEM4 M=M =L AC30;00300@ <=3 E>6A>=B>9 8EMMEM= 048; 79; 134 109=30 402B0340E 1>;><639 18;MM. "0=:=K M@A4M;89= C48@4;030" 3M4M3 AM4M2 =L @ <0H @3= E@MM=89 0ACC4;K3 E0<0@A0= 0ACC40; CG8@ 5@=E894 =L AC4;0E00A00 8; =M36 EMA3MM@ =L AC40;6 =M;3MM 43=M;B 3G 109E =L 8; @ 4=4 E@=M. 9< CG@00A M@A4M;893 <0H >;>= B@; 0=38;0;4 EC2006 74M3 134 0=38;0; 1@89= 1093CC;;0304 7;ME =;3 BCA309;0= AC40;6 109=0. 8=89 185 M=ME 48?;><K= 06;00@ 10=: A0=E389= 1093CC;;0304 B>E8>;44>3 M@A4M;4893 B>4@CC;6 B=89 4>B>@ 70E 77M;89= M@A4M;89= B><>>E>= EMAM3 1>;>E E0=H89= M@A4M;MMA AM@389;6 1>;>E 70320@ VAR / value at risk /-K3 =4MA;M= 52@>389= E0=H8=4 AC40;300, H8=68;3MM E896 <>45;L /70320@/ 30@306 02;00. EURO = -11.98119732 - 0.001713214601*" + 1.512346482E-07*("^2) + 2.102372787*LOG(T) + 157.4637276*(1/") + [AR(l)=0.9970263182] -=ME 70320@K3 30@306 020E04 40@00E =4AM= 79;A893 0H83;0A0=: 1986 >=>>A =4@893 E@BM;E 52@>389= E0=H 95 EC289= 8B3ME 702A0@B 1>4>34A>= !0=E389= EViews ?@>3@0<< E0=30<6 =3MA=MM@ 30@306 02A0= 70320@B 8B3ME, 70320@K= 0G E>;1>34;K= B2H8=3 =M<M34;6 109300 18;MM. H83;0A0= <0B5@80;K= 603A00;B "0E 7MM;89= M@A4M; B>>F>E 0@30G;0;" >=3>; 10=: %O=0;B H0;30;BK= 3070@, #-2003.9-11 "9; 068;;0300=K M@A4M;89= C48@4;03K= =4AM= 70@G<CC4K= B0;00@ 10=: A0=E389= 1093CC;;03CC404 3A= 72;<6" >=3>; 10=: 2005 >= "EViews" .=EBCO0, '.0@0=G8<M3 "-@A4M; 10 400B30;" .0;6 2006 Basel Committee on Banking Supervision, www.bis.org Crouhy, M, Mark, R. and Galai, D., 2000, "Risk Management," McGraw-Hill Trade. Harmantzis, C. F., 2002, "Methodologies for Management and Measuring Operational Risk," INFORMS Annual Meeting 2002 San Jose, Calif. Jorion, P., 2000, "Value at Risk: The New Benchmark for Managing Financial Risk," McGraw-Hill Trade. Cruz, M., Coleman, R. and Salkin, G., 1998, "Modeling and Measuring Operational Risk," Journal of Risk, Vol. 1, pg. 63-72. Operational Risk Special Report, 2000, Risk, November 2000.      PAGE  PAGE 49    IV . 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