Total Return Swap 1997 7 J.P. Morgan TRSTotal Return Swap 1998 10 J.P. Morgan 75800 1996 1997 J.P. Morgan SK LG 17100 SK 16129 12593 10235 8150 7300 19981023 1
J.P. Morgan 27550 1 48250 75800 TRS SK SK 1998 2 11 J.P. Morgan J.P. Morgan SK SK J.P. Morgan TRS 1. TRS 1.1. J.P. Morgan TRSTotal Return Swap TRS 1990 credit derivatives total return J.P. Morgan Total Return 2
J.P. Morgan 4550 Total Return J.P. Morgan J.P. Morgan J.P. Morgan Total Return J.P. Morgan J.P. Morgan J.P. Morgan 1 minus funding J.P. Morgan 1.2. 1997 3 J.P. Morgan TRS 1 4550 TRS 1997 3 16 1998 3 16 1997 3 3 US45500000 US$ 45, 500, 000[ 1 1% Max{ 0, ( Ym Ys )/ Ym} 5{( s m)/ m}] US$ 45, 500, 000{( K m K s )/ K m} 1 Y s 12164 s 25935 K s 87796 Y m s K s 3
TRS 1997 2 12 1998 2 12 1997 1 29 US53000000 US$53,000,000[1 3% Max{0, (Y m Y s )/Y m } Min{1, 5( s m )/ m }] 2 Y S 122 S 25884 1997 1 29SKLG 3440 J.P. Morgan TRS 1 5300 8650 1 1 7 1 / / Max{ 0, ( )/ } Max 0, 1 Y Y Y Y s 1 Ym Y m s m = = Max{ 0, r } 1/ Ys 3 1/ 1/ 5 {( )/ } 5 m s s m m = 1/ s = 5r 4 1/ K 1/ 0. 989 {( K K )/ K } 0. 989 s K m K m s m = = 0. 989 r 1/ K s 5 r Y r r K USD/JPYUSD/THUSD/KRW 1 Max{0, (Y m Y s )/Y m } = Y s Max{0, (1/Y s 1/Y m )} 6 1Y s Y s 1 4
1 %/USD 1/121.64 USD/JPY XUSD/JPY %/USD 5 1/25.935 USD/TH X USDTH 2 5{( s m )/ m }=5 s (1/ m 1/ s ) 7 1 s 5 s 1 %/USD 1/877.96 USD/KRW XUSDKRW 5
1 3 K s 0989K s 1 0.989{(K m K s )/K m } = 0.989K s (1/K s 1/K m ) 1.3. 1997 2 14 1997 7 2 1) 25 5 1998 3 40 4 5 1 300 250 200 JPY/USD 150 100 50 0 1986 1988 1990 1992 1994 1996 1998 Year 1985319983 1 1984 11 6
60 50 TH/USD 40 30 20 10 0 1986 1988 1990 1992 1994 1996 1998 Year 1985319983 KRW/USD 2,000 1,800 1,600 1,400 1,200 1,000 800 600 400 200 0 1986 1988 1990 1992 1994 1996 1998 Year 1985319983 5 J.P. Morgan 1 TRS 4550 230 130 6 40 177 1997 7 TRS 7
1997 3 1 0 0 0 99 4 1 4 2 2 95 5 1 0 11 2 86 6 1 0 40 1 58 7 1 0 69 2 166 8 1 0 94 2 191 9 1 0 133 4 228 10 1 0 152 4 247 11 1 4 162 11 246 12 1 7 226 48 270 1998 1 1 7 251 45 298 2 1 3 222 45 273 3 1 6 177 40 230 11 = 1 minus funding 15 1.4. 1TRS J.P. Morgan 2TRS 150989 2 J.P. Morgan 3VaRValue at Risk 8
2 VaR TRS 4 J.P. Morgan 2. J.P. Morgan 2.1. 1985 5 1997 2 2 OLS 2 7 2 15 1098 1 J.P. Morgan 1 TRS OLS β 454 098 023 R 2 66 5 32 ρ 081 018 022 9
1minus funding Y t1 Y t Y t1 r t Y = 5r t r t Y = 0.989r t K 5r t 0.989 r t K = r t Y r t Y = J.P. Morgan TRS 1997 3 J.P. Morgan TRS 3 2.2. TRS 1997 3 8 10
1 2725 THUSD 93175 KRWUSD1997 3 1 611115 25935 THUSD87796 KRWUSD J.P. Morgan TRS 14-1 5 s (1/ m 1/ s ) + 0.989K s (1/K s 1/K m ) 5 s (1/ f 1/ m ) + 0.989K s (1/K m 1/K f ) 1 5 s (1/ f 1/ s ) + 0.989K s (1/K s 1/K f ) 13 246 14 25 3 24 6 TRS 8 6 14 5 1 minus funding 5 3 1 3 1 3. TRS J.P. Morgan 1 5 0989 3.1. TRS 11
1 2 1985 5 1997 2 bootstrapping method 2 142 12 1 10000 10000 TRS 150989 1 0989 5 TRS P P = Max(0, r Y ) + h r h K r K h h K P h K = 0.989 dvar ( P ) K Y 0 Cov r r Cov Max r r h. 989 (, ) [ ( 0, = 0 ), ] = 4 dh Var( r ) TRS P K [ Ys Max{ 0, ( 1/ Ys 1/ Ym)} + h r hk r ] = Ys Max{ 0, ( 1/ Ys 1/ Y Y K m)} = + h h Y K Ys Put Y K Y K = + h h Ys Y K = δ + h ( 1/ m) hk 12
δ 3 3 t 1001 0759 0506 0253 000 δ 01610 02031 02589 03371 04936 3 0.16101 0.20310.75 0.25890.5 0.33710.25 0.49360.0001 δ = = 0.2108 1 + 0.75 + 0.5 + 0.25 + 0.0001 h K = 0.989 Y K h = 0. 2108 + 0. 989 = 0. 88 3.2. VaR Value at RiskVaR VaR 10000 10000 100 99 VaR TRS 8 99 VaR 137 37 100 4 VaR 133 088 VaR 124 VaR 5 13
0.04 0.03 Mean: 99% SD: 13.8 % Mode: 94 % VaR (99): 137 % Prob 0.02 0.01 0.00 40 80 120 160 200 Redemption (%) 4. 4.1. 1997 2 1997 3 TRS VaR 4 1985 1997 10 25 0 J.P. Morgan 3242 100 14
1 177 Max 1, 5 s m m J.P. Morgan J.P. Morgan Early Termination 7 1997 8 1 6 3304 5 s f s 108 1 6 40 161 230 4.2. 1989 10 30 1 300 1996 3 29 600 1 TRS 1997 3 980 380 1997 15
1997 12 19 1998 2 18 1998 5 27 J.P. Morgan RiskMetrics VaR front-office back-office middle-office VaR 16
3 ============ 8: 1997 3 31 7: 1996 3 31 6: 1995 3 31 (: ) 8 7 6 I. 462,387 358,273 459,997 (1) 462,387 356,138 454,169 1. 16,362 4,674 21,965 2. 427,412 341,061 414,890. 86,257 52,836 55,993 (1) 65,569 32,890 36,243 (2) 20,626 19,822 19,750 (3) 62 124 548,644 411,109 515,990 I. 587,629 392,234 500,707 1. 579,800 370,760 477,090. 4,977 4,988 3,482 1. 4,977 4,988 3,482 592,606 397,222 504,189 I. 60,000 60,000 30,000. (103,962) (46,113) (18,199) (43,962) 13,887 11,801 548,644 411,109 515,990 17
=========== 8: 1996 4 1 1997 3 31 7: 1995 4 1 1996 3 31 6: 1994 4 1 1995 3 31 ( : ) 8 7 6 I. 57,041 65,216 69,830. 55,962 38,008 47,870. 1,079 27,208 21,960. 2,154 2,004 1,975. 61,065 57,038 40,340 (1) 60,926 56,892 40,279 (2) 139 146 61. 57,832 27,826 16,405. 12 - -. 29 50 16. 57,849 27,876 16,421. - - -. 57,849 27,876 16,421 : 97,842 60,202 36,977 18
1985 51997 2 http://www.bog.frb.us/releases/h10/hist/ 05/01/85 252.75 27.55 867.7 05/01/89 134.07 25.53 669.0 05/03/93 110.90 25.23 799.1 06/03/85 248.60 27.55 873.1 06/01/89 142.73 25.92 669.3 06/01/93 107.23 25.13 805.4 07/01/85 247.95 27.38 876.0 07/03/89 141.25 25.90 669.9 07/01/93 107.85 25.33 806.4 08/01/85 237.65 26.77 878.3 08/01/89 136.82 25.69 670.0 08/02/93 104.35 25.27 809.8 09/02/85 239.00 26.88 887.3 09/01/89 145.85 26.01 672.2 09/01/93 105.70 25.20 811.3 10/01/85 215.00 26.37 894.0 10/02/89 139.48 25.78 672.7 10/01/93 106.05 25.26 812.0 11/01/85 209.00 26.44 894.2 11/01/89 143.11 25.88 674.4 11/01/93 108.28 25.37 811.4 12/02/85 204.03 26.24 891.4 12/01/89 143.10 25.81 675.3 12/01/93 108.70 25.45 811.0 01/01/86 200.25 26.70 892.5 01/01/90 143.80 25.71 681.4 01/03/94 112.50 25.58 810.4 02/03/86 191.55 26.55 890.6 02/01/90 144.90 25.72 689.5 02/01/94 108.05 25.41 812.0 03/03/86 179.65 26.37 886.6 03/01/90 149.67 25.85 696.7 03/01/94 104.80 25.35 811.2 04/01/86 178.15 26.46 887.1 04/02/90 158.90 26.07 704.9 04/01/94 103.75 25.25 810.4 05/01/86 169.65 26.30 887.9 05/01/90 158.85 26.00 709.2 05/02/94 101.79 25.19 810.7 06/02/86 174.90 26.56 892.1 06/01/90 151.39 25.89 714.1 06/01/94 104.70 25.22 809.3 07/01/86 162.70 26.30 888.4 07/02/90 151.27 25.78 718.8 07/01/94 98.51 25.04 808.3 08/01/86 153.85 26.12 888.4 08/01/90 147.25 25.59 716.9 08/01/94 99.35 24.97 805.8 09/01/86 154.55 26.16 885.1 09/03/90 143.93 25.49 716.8 09/01/94 99.63 25.03 803.3 10/01/86 154.15 26.11 881.0 10/01/90 136.90 25.33 715.7 10/03/94 99.50 25.02 801.3 11/03/86 164.00 26.32 877.5 11/01/90 130.48 25.14 716.4 11/01/94 96.77 24.91 800.2 12/01/86 162.25 26.21 868.9 12/03/90 134.40 25.17 715.8 12/01/94 99.40 25.06 797.6 01/01/87 158.30 26.27 865.2 01/01/91 135.75 25.31 719.2 01/02/95 99.60 25.11 792.7 02/02/87 152.57 25.94 861.8 02/01/91 131.45 25.16 721.5 02/01/95 99.40 25.07 789.8 03/02/87 153.50 25.73 858.7 03/01/91 134.55 25.27 727.2 03/01/95 96.75 24.95 789.1 04/01/87 146.82 25.77 850.8 04/01/91 140.20 25.63 727.5 04/03/95 86.25 24.62 774.4 05/01/87 140.35 25.59 838.0 05/01/91 137.60 25.67 727.3 05/01/95 83.53 24.60 764.8 06/01/87 145.45 25.75 826.5 06/03/91 139.08 25.69 725.4 06/01/95 84.95 24.69 762.0 07/01/87 146.85 25.82 812.7 07/01/91 138.40 25.77 725.9 07/03/95 84.80 24.68 761.0 08/03/87 150.50 25.99 811.7 08/01/91 137.67 25.72 728.7 08/01/95 88.43 24.77 760.1 09/01/87 141.83 25.80 811.3 09/02/91 136.85 25.74 736.7 09/01/95 97.49 25.05 773.2 10/01/87 146.90 25.90 809.5 10/01/91 133.20 25.56 746.0 10/02/95 100.72 25.14 768.4 11/02/87 137.00 25.59 805.1 11/01/91 130.30 25.58 756.4 11/01/95 103.07 25.21 766.1 12/01/87 133.00 25.36 799.7 12/02/91 129.95 25.48 759.0 12/01/95 101.20 25.16 770.0 01/01/88 121.25 25.09 795.9 01/01/92 124.90 25.40 765.3 01/01/96 103.28 25.20 775.8 02/01/88 129.38 25.25 785.2 02/03/92 125.95 25.40 766.8 02/01/96 107.08 25.34 784.8 03/01/88 128.27 25.32 764.3 03/02/92 129.63 25.53 772.4 03/01/96 105.70 25.22 782.8 04/01/88 124.00 25.16 748.1 04/01/92 134.50 25.62 779.6 04/01/96 107.53 25.27 781.7 05/02/88 124.95 25.15 743.4 05/01/92 132.75 25.64 783.0 05/01/96 105.08 25.27 778.3 06/01/88 125.20 25.22 736.3 06/01/92 127.45 25.42 788.2 06/03/96 108.37 25.34 785.8 07/01/88 134.10 25.49 731.4 07/01/92 124.92 25.30 793.2 07/01/96 109.56 25.38 809.9 08/01/88 132.80 25.56 726.7 08/03/92 127.28 25.31 790.3 08/01/96 106.75 25.25 813.2 09/01/88 136.35 25.61 725.0 09/01/92 122.95 25.13 788.9 09/02/96 108.70 25.32 819.3 10/03/88 133.65 25.54 721.9 10/01/92 120.00 25.15 788.3 10/01/96 111.37 25.43 821.0 11/01/88 125.30 25.25 702.7 11/02/92 123.95 25.41 785.5 11/01/96 113.28 25.51 827.0 12/01/88 121.60 25.07 689.8 12/01/92 124.40 25.53 787.8 12/02/96 113.80 25.55 832.0 01/02/89 125.05 25.20 687.4 01/01/93 124.85 25.53 791.5 01/01/97 115.77 25.65 847.5 02/01/89 129.60 25.45 683.5 02/01/93 124.95 25.55 797.1 02/03/97 121.68 25.90 869.0 03/01/89 128.10 25.38 675.8 03/01/93 118.75 25.47 798.0 04/03/89 132.05 25.55 673.7 04/01/93 114.10 25.34 797.1 19