Modell A B C D 1 4.0 3.4 2.9 2.7 2 5.4 4.3 3.8 3.6 3 8.2 6.2 5.4 5.3 4 10.9 8.5 7.6 7.4 5 14.9 11.7 11.0 11.1 6 22.8 19.0 19.1 20.7
Tabelle A.3.: tatsächliche Werte ES Modelltyp LogLog
Modell A B C D
Quantil Wert Rel. Fehler Wert Rel. Fehler Wert Rel. Fehler Wert Rel. Fehler
1 5% 157,265 93% 290,778 87% 412,629 80% 563,577 72%
95% 15,670,006 566% 13,508,683 524% 12,601,149 506% 8,710,710 334%
2 5% 337,305 90% 606,242 79% 877,561 68% 1,092,125 60%
95% 28,957,436 778% 24,650,012 754% 10,900,777 292% 8,222,833 198%
3 5% 983,174 81% 1,667,341 62% 2,153,160 49% 2,477,518 42%
95% 26,222,045 410% 21,557,338 396% 11,626,534 176% 7,963,684 86%
4 5% 2,323,502 67% 3,164,347 49% 3,843,907 37% 4,423,339 30%
95% 39,089,889 447% 13,560,594 116% 11,208,068 85% 9,990,079 58%
5 5% 4,271,842 58% 5,370,308 41% 6,679,512 28% 7,938,990 19%
95% 36,624,385 260% 18,684,078 107% 12,967,831 40% 13,379,782 36%
6 5% 9,824,910 42% 11,929,889 25% 14,401,306 16% 17,031,779 11%
95% 33,947,318 102% 22,252,593 40% 20,762,961 21% 22,211,164 16%
Tabelle A.4.: Übersicht über die relativen Fehler VaR, Modelltyp LogLog
Modell A B C D
Quantil Wert Rel. Fehler Wert Rel. Fehler Wert Rel. Fehler Wert Rel. Fehler
1 5% 178,852 95% 327,720 90% 480,678 83% 653,890 76%
95% 48,447,475 1125% 35,261,881 950% 27,571,060 856% 15,290,471 468%
2 5% 381,952 93% 691,666 84% 1,018,984 73% 1,224,346 66%
95% 86,555,455 1513% 60,896,492 1325% 18,749,790 389% 12,842,291 260%
3 5% 1,171,109 86% 1,967,135 68% 2,529,886 54% 2,795,704 47%
95% 67,743,063 724% 45,692,076 637% 18,675,368 243% 10,881,190 107%
4 5% 2,832,274 74% 3,691,623 57% 4,359,578 42% 4,872,803 34%
95% 95,039,080 769% 21,552,739 154% 16,040,468 112% 12,845,332 73%
5 5% 5,145,283 66% 6,245,114 46% 7,492,867 32% 8,686,505 22%
95% 73,319,329 391% 27,635,581 137% 16,561,796 50% 16,139,444 46%
6 5% 12,218,481 46% 13,570,116 29% 15,579,896 19% 18,009,796 13%
95% 54,379,623 139% 29,251,530 54% 24,611,867 29% 24,224,767 17%
Tabelle A.5.: Übersicht über die relativen Fehler ES, Modelltyp LogLog
Modell A B C D
Lognormal µ 8.33 E+0 8.19 E+0 9.71 E+0 1.01 E+1 σ 1.78 E+0 1.50 E+0 1.33 E+0 1.20 E+0
Tabelle A.6.: Parameter der Lognormalverteilung, Modelltyp LogLog
139
Spalte A, E=20.000
λ = 8.33, σ = 1.78Der Erwartungswert eines Verlustes beträgt also 20.000. Das 99.9%-Quantil eines Verlustest beträgt 1.000.000.
Zeile 1, λ=5
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.1.:Modell LogLog, Ergeb-nis A1, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
98,716 242,802
597,196 1,468,864
3,612,823 8,886,111
21,856,305 53,757,836
132,222,9 41
325,215,9 56
799,902,1 77
größer
Klassenobergrenze
Anteil
Abbildung A.2.:Modell LogLog, Ergeb-nis A1, VaR
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.3.:Modell LogLog, Ergeb-nis A1, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
109,098 362,217
1,202,604 3,992,787
13,256,51 9
44,013,19 4
146,128,9 49
485,165,1 95
1,610,805 ,176
5,348,061 ,523
17,756,18 9,566
größer
Klassenobergrenze
Anteil
Abbildung A.4.:Modell LogLog, Ergeb-nis A1, ES
Zeile 2, λ=10
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.5.:Modell LogLog, Ergeb-nis A2, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
162,755 327,748
660,003 1,329,083
2,676,445 5,389,698
10,853,520 21,856,305
44,013,194 88,631,688
178,482,3 01
größer
Klassenobergrenze
Anteil
Abbildung A.6.:Modell LogLog, Ergeb-nis A2, VaR
Wahrer Wert
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.7.:Modell LogLog, Ergeb-nis A2, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
179,872 400,312
890,911 1,982,759
4,412,712 9,820,671
21,856,30 5
48,642,10 2
108,254,988 240,925,906
536,190,464 größer
Klassenobergrenze
Anteil
Abbildung A.8.:Modell LogLog, Ergeb-nis A2, ES
Zeile 3, λ=25
Wahrer Wert
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.9.:Modell LogLog, Ergeb-nis A3, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
597,196 984,609 1,623,346 2,676,445 4,412,712 7,275,332 11,994,995 19,776,403 32,605,776 53,757,836 88,631,688 größer Klassenobergrenze
Anteil
Abbildung A.10.: Modell LogLog, Er-gebnis A3, VaR
141
Wahrer Wert
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000 8,000,000 9,000,000 10,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.11.: Modell LogLog, Er-gebnis A3, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
729,416 1,342,441
2,470,670 4,547,099
8,368,624 15,401,878
28,346,100 52,169,052
96,013,561 176,706,3
72
325,215,9 56
größer
Klassenobergrenze
Anteil
Abbildung A.12.: Modell LogLog, Er-gebnis A3, ES
Zeile 4, λ=50
Wahrer Wert
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000 8,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.13.: Modell LogLog, Er-gebnis A4, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
984,609 1,623,346
2,676,445 4,412,712
7,275,332 11,994,995
19,776,403 32,605,776
53,757,836 88,631,688
146,128,9 49
größer
Klassenobergrenze
Anteil
Abbildung A.14.: Modell LogLog, Er-gebnis A4, VaR
Wahrer Wert
0 2,000,000 4,000,000 6,000,000 8,000,000 10,000,000 12,000,000 14,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.15.: Modell LogLog, Er-gebnis A4, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
1,202,604 2,126,526
3,760,265 6,649,153
11,757,47 8
20,790,36 1
36,762,90 9
65,006,64 2
114,949,1 02
203,260,7 10
359,419,2 17
größer
Klassenobergrenze
Anteil
Abbildung A.16.: Modell LogLog, Er-gebnis A4, ES
Zeile 5, λ=100
Wahrer Wert
0 2,000,000 4,000,000 6,000,000 8,000,000 10,000,000 12,000,000 14,000,000 16,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.17.: Modell LogLog, Er-gebnis A5, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
3,269,017 4,876,801
7,275,332 10,853,520
16,191,549 24,154,953
36,034,955 53,757,836
80,197,267 119,640,2
64
178,482,3 01
größer
Klassenobergrenze
Anteil
Abbildung A.18.: Modell LogLog, Er-gebnis A5, VaR
Wahrer Wert
0 2,000,000 4,000,000 6,000,000 8,000,000 10,000,000 12,000,000 14,000,000 16,000,000 18,000,000 20,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.19.: Modell LogLog, Er-gebnis A5, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
3,992,787 6,388,436
10,221,46 0
16,354,27 7
26,166,74 8
41,866,64 5
66,986,38 9
107,177,833 171,483,910
274,373,260 438,995,623
größer
Klassenobergrenze
Anteil
Abbildung A.20.: Modell LogLog, Er-gebnis A5, ES
Zeile 6, λ=250
Wahrer Wert
0 5,000,000 10,000,000 15,000,000 20,000,000 25,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.21.: Modell LogLog, Er-gebnis A6, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
40%
6,582,993 8,886,111
11,994,99 5
16,191,54 9
21,856,30 5
29,502,92 6
39,824,78 4
53,757,83 6
72,565,48 8
97,953,16 4
132,222,9 41
größer
Klassenobergrenze
Anteil
Abbildung A.22.: Modell LogLog, Er-gebnis A6, VaR
143
Wahrer Wert
0 5,000,000 10,000,000 15,000,000 20,000,000 25,000,000 30,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.23.: Modell LogLog, Er-gebnis A6, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
8,040,485 10,853,520
14,650,719 19,776,403
26,695,351 36,034,955
48,642,102 65,659,969
88,631,688 119,640,2
64
161,497,4 64
größer
Klassenobergrenze
Anteil
Abbildung A.24.: Modell LogLog, Er-gebnis A6, ES
Spalte B, E=30.000
λ = 9.19, σ = 1.50Der Erwartungswert eines Verlustes beträgt also 30.000. Das 99.9%-Quantil eines Verlustest beträgt 1.000.000.
Zeile 1, λ=5
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.25.: Modell LogLog, Er-gebnis B1, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
162,755 327,748
660,003 1,329,083
2,676,445 5,389,698
10,853,52 0
21,856,30 5
44,013,19 4
88,631,68 8
178,482,3 01
größer
Klassenobergrenze
Anteil
Abbildung A.26.: Modell LogLog, Er-gebnis B1, VaR
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.27.: Modell LogLog, Er-gebnis B1, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
179,872 400,312
890,911 1,982,759
4,412,712 9,820,671
21,856,305 48,642,102
108,254,9 88
240,925,9 06
536,190,4 64
größer
Klassenobergrenze
Anteil
Abbildung A.28.: Modell LogLog, Er-gebnis B1, ES
Zeile 2, λ=10
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.29.: Modell LogLog, Er-gebnis B2, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
327,748 597,196
1,088,161 1,982,759
3,612,823 6,582,993
11,994,995 21,856,305
39,824,784 72,565,488
132,222,9 41
größer
Klassenobergrenze
Anteil
Abbildung A.30.: Modell LogLog, Er-gebnis B2, VaR
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000 5,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.31.: Modell LogLog, Er-gebnis B2, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
327,748 729,416
1,623,346 3,612,823
8,040,485 17,894,42
9
39,824,78 4
88,631,68 8
197,253,4 48
438,995,6 23
977,002,7 26
größer
Klassenobergrenze
Anteil
Abbildung A.32.: Modell LogLog, Er-gebnis B2, ES
145
Zeile 3, λ=25
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000 5,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.33.: Modell LogLog, Er-gebnis B3, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
984,609 1,623,346
2,676,445 4,412,712
7,275,332 11,994,995
19,776,403 32,605,776
53,757,836 88,631,688
146,128,9 49
größer
Klassenobergrenze
Anteil
Abbildung A.34.: Modell LogLog, Er-gebnis B3, VaR
Wahrer Wert
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.35.: Modell LogLog, Er-gebnis B3, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
1,088,161 1,867,292
3,204,286 5,498,578
9,435,597 16,191,54
9
27,784,80 9
47,678,92 3
81,817,36 0
140,399,151 240,925,906
größer
Klassenobergrenze
Anteil
Abbildung A.36.: Modell LogLog, Er-gebnis B3, ES
Zeile 4, λ=50
Wahrer Wert
5,200,000 5,400,000 5,600,000 5,800,000 6,000,000 6,200,000 6,400,000 6,600,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.37.: Modell LogLog, Er-gebnis B4, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
2,191,288 2,957,929 3,992,787 5,389,698 7,275,332 9,820,671 13,256,519 17,894,429 24,154,953 32,605,776 44,013,194 größer Klassenobergrenze
Anteil
Abbildung A.38.: Modell LogLog, Er-gebnis B4, VaR
Wahrer Wert
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000 8,000,000 9,000,000 10,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.39.: Modell LogLog, Er-gebnis B4, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
2,421,748 3,760,265
5,838,591 9,065,622
14,076,257 21,856,305
33,936,443 52,693,360
81,817,360 127,038,4
05
197,253,4 48
größer
Klassenobergrenze
Anteil
Abbildung A.40.: Modell LogLog, Er-gebnis B4, ES
Zeile 5, λ=100
Wahrer Wert
0 2,000,000 4,000,000 6,000,000 8,000,000 10,000,000 12,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.41.: Modell LogLog, Er-gebnis B5, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
40%
3,992,787 5,389,698 7,275,332 9,820,671 13,256,519 17,894,429 24,154,953 32,605,776 44,013,194 59,411,597 80,197,267 größer Klassenobergrenze
Anteil
Abbildung A.42.: Modell LogLog, Er-gebnis B5, VaR
Wahrer Wert
0 2,000,000 4,000,000 6,000,000 8,000,000 10,000,000 12,000,000 14,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.43.: Modell LogLog, Er-gebnis B5, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
40%
4,876,801 6,851,650
9,626,209 13,524,31
9
19,000,95 9
26,695,35 1
37,505,57 0
52,693,36 0
74,031,40 8
104,010,2 49
146,128,9 49
größer
Klassenobergrenze
Anteil
Abbildung A.44.: Modell LogLog, Er-gebnis B5, ES
147
Zeile 6, λ=250
Wahrer Wert
14,000,000 14,500,000 15,000,000 15,500,000 16,000,000 16,500,000 17,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.45.: Modell LogLog, Er-gebnis B6, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
9,820,671 11,409,992 13,256,519 15,401,878 17,894,429 20,790,361 24,154,953 28,064,051 32,605,776 37,882,507 44,013,194 größer Klassenobergrenze
Anteil
Abbildung A.46.: Modell LogLog, Er-gebnis B6, VaR
Wahrer Wert
0 5,000,000 10,000,000 15,000,000 20,000,000 25,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.47.: Modell LogLog, Er-gebnis B6, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
11,994,995 14,076,257 16,518,640 19,384,804 22,748,278 26,695,351 31,327,285 36,762,909 43,141,674 50,627,223 59,411,597 größer Klassenobergrenze
Anteil
Abbildung A.48.: Modell LogLog, Er-gebnis B6, ES
Spalte C, E=40.000
λ = 9.72, σ = 1.33Der Erwartungswert eines Verlustes beträgt also 40.000. Das 99.9%-Quantil eines Verlustest beträgt 1.000.000.
Zeile 1, λ=5
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.49.: Modell LogLog, Er-gebnis C1, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
242,802 442,413 806,130 1,468,864 2,676,445 4,876,801 8,886,111 16,191,549 29,502,926 53,757,836 97,953,164 größer Klassenobergrenze
Anteil
Abbildung A.50.: Modell LogLog, Er-gebnis C1, VaR
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.51.: Modell LogLog, Er-gebnis C1, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
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30%
268,337 540,365
1,088,161 2,191,288
4,412,712 8,886,111
17,894,42 9
36,034,95 5
72,565,48 8
146,128,949 294,267,566
größer
Klassenobergrenze
Anteil
Abbildung A.52.: Modell LogLog, Er-gebnis C1, ES
Zeile 2, λ=10
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.53.: Modell LogLog, Er-gebnis C2, VaR, Wahrer Wert
Histogramm
0%
5%
10%
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25%
30%
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488,942 806,130 1,329,083 2,191,288 3,612,823 5,956,538 9,820,671 16,191,549 26,695,351 44,013,194 72,565,488 größer Klassenobergrenze
Anteil
Abbildung A.54.: Modell LogLog, Er-gebnis C2, VaR
149
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.55.: Modell LogLog, Er-gebnis C2, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
488,942 882,046
1,591,202 2,870,509
5,178,365 9,341,711
16,852,339 30,401,424
54,843,816 98,937,609
178,482,3 01
größer
Klassenobergrenze
Anteil
Abbildung A.56.: Modell LogLog, Er-gebnis C2, ES
Zeile 3, λ=25
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000 5,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.57.: Modell LogLog, Er-gebnis C3, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
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40%
1,329,083 1,982,759 2,957,929 4,412,712 6,582,993 9,820,671 14,650,719 21,856,305 32,605,776 48,642,102 72,565,488 größer Klassenobergrenze
Anteil
Abbildung A.58.: Modell LogLog, Er-gebnis C3, VaR
Wahrer Wert
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.59.: Modell LogLog, Er-gebnis C3, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
1,468,864 2,258,023
3,471,162 5,336,070
8,202,914 12,609,99
1
19,384,80 4
29,799,43 5
45,809,40 6
70,420,85 4
108,254,9 88
größer
Klassenobergrenze
Anteil
Abbildung A.60.: Modell LogLog, Er-gebnis C3, ES
Zeile 4, λ=50
Wahrer Wert
5,200,000 5,300,000 5,400,000 5,500,000 5,600,000 5,700,000 5,800,000 5,900,000 6,000,000 6,100,000 6,200,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.61.: Modell LogLog, Er-gebnis C4, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
2,676,445 3,269,017 3,992,787 4,876,801 5,956,538 7,275,332 8,886,111 10,853,520 13,256,519 16,191,549 19,776,403 größer Klassenobergrenze
Anteil
Abbildung A.62.: Modell LogLog, Er-gebnis C4, VaR
Wahrer Wert
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000 8,000,000 9,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.63.: Modell LogLog, Er-gebnis C4, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
2,957,929 3,798,056 4,876,801 6,261,936 8,040,485 10,324,187 13,256,519 17,021,708 21,856,305 28,064,051 36,034,955 größer Klassenobergrenze
Anteil
Abbildung A.64.: Modell LogLog, Er-gebnis C4, ES
Zeile 5, λ=100
Wahrer Wert
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000 8,000,000 9,000,000 10,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.65.: Modell LogLog, Er-gebnis C5, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
5,389,698 6,261,936 7,275,332 8,452,730 9,820,671 11,409,992 13,256,519 15,401,878 17,894,429 20,790,361 24,154,953 größer Klassenobergrenze
Anteil
Abbildung A.66.: Modell LogLog, Er-gebnis C5, VaR
151
Wahrer Wert
0 2,000,000 4,000,000 6,000,000 8,000,000 10,000,000 12,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.67.: Modell LogLog, Er-gebnis C5, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
5,956,538 7,275,332 8,886,111 10,853,520 13,256,519 16,191,549 19,776,403 24,154,953 29,502,926 36,034,955 44,013,194 größer Klassenobergrenze
Anteil
Abbildung A.68.: Modell LogLog, Er-gebnis C5, ES
Zeile 6, λ=250
Wahrer Wert
15,800,000 16,000,000 16,200,000 16,400,000 16,600,000 16,800,000 17,000,000 17,200,000 17,400,000 17,600,000 17,800,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.69.: Modell LogLog, Er-gebnis C6, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
9,820,671 10,853,520 11,994,995 13,256,519 14,650,719 16,191,549 17,894,429 19,776,403 21,856,305 24,154,953 26,695,351 größer Klassenobergrenze
Anteil
Abbildung A.70.: Modell LogLog, Er-gebnis C6, VaR
Wahrer Wert
16,000,000 16,500,000 17,000,000 17,500,000 18,000,000 18,500,000 19,000,000 19,500,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.71.: Modell LogLog, Er-gebnis C6, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
14,650,719 15,870,935 17,192,779 18,624,715 20,175,912 21,856,305 23,676,653 25,648,612 27,784,809 30,098,925 32,605,776 größer Klassenobergrenze
Anteil
Abbildung A.72.: Modell LogLog, Er-gebnis C6, ES
Spalte D, E=50.000
λ= 10.10,σ = 1.20Der Erwartungswert eines Verlustes beträgt also50.000. Das 99.9%-Quantil eines Verlustest beträgt 1.000.000.
Zeile 1, λ=5
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.73.: Modell LogLog, Er-gebnis D1, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
242,802 442,413 806,130 1,468,864 2,676,445 4,876,801 8,886,111 16,191,549 29,502,926 53,757,836 97,953,164 größer Klassenobergrenze
Anteil
Abbildung A.74.: Modell LogLog, Er-gebnis D1, VaR
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.75.: Modell LogLog, Er-gebnis D1, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
400,312 806,130
1,623,346 3,269,017
6,582,993 13,256,51
9
26,695,35 1
53,757,83 6
108,254,9 88
217,998,7 75
438,995,6 23
größer
Klassenobergrenze
Anteil
Abbildung A.76.: Modell LogLog, Er-gebnis D1, ES
153
Zeile 2, λ=10
Wahrer Wert
2,400,000 2,450,000 2,500,000 2,550,000 2,600,000 2,650,000 2,700,000 2,750,000 2,800,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.77.: Modell LogLog, Er-gebnis D2, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
729,416 1,088,161 1,623,346 2,421,748 3,612,823 5,389,698 8,040,485 11,994,995 17,894,429 26,695,351 39,824,784 größer Klassenobergrenze
Anteil
Abbildung A.78.: Modell LogLog, Er-gebnis D2, VaR
Wahrer Wert
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.79.: Modell LogLog, Er-gebnis D2, ES, Wahrer Wert
Histogramm
0%
5%
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15%
20%
25%
890,911 1,342,441 2,022,814 3,048,012 4,592,798 6,920,510 10,427,947 15,713,016 23,676,653 35,676,401 53,757,836 größer Klassenobergrenze
Anteil
Abbildung A.80.: Modell LogLog, Er-gebnis D2, ES
Zeile 3, λ=25
Wahrer Wert
4,200,000 4,250,000 4,300,000 4,350,000 4,400,000 4,450,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.81.: Modell LogLog, Er-gebnis D3, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
1,794,075 2,191,288 2,676,445 3,269,017 3,992,787 4,876,801 5,956,538 7,275,332 8,886,111 10,853,520 13,256,519 größer Klassenobergrenze
Anteil
Abbildung A.82.: Modell LogLog, Er-gebnis D3, VaR
Wahrer Wert
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000 8,000,000 9,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.83.: Modell LogLog, Er-gebnis D3, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
1,982,759 2,545,913 3,269,017 4,197,501 5,389,698 6,920,510 8,886,111 11,409,992 14,650,719 18,811,896 24,154,953 größer Klassenobergrenze
Anteil
Abbildung A.84.: Modell LogLog, Er-gebnis D3, ES
Zeile 4, λ=50
Wahrer Wert
5,500,000 5,600,000 5,700,000 5,800,000 5,900,000 6,000,000 6,100,000 6,200,000 6,300,000 6,400,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.85.: Modell LogLog, Er-gebnis D4, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
35%
2,957,929 3,612,823 4,412,712 5,389,698 6,582,993 8,040,485 9,820,671 11,994,995 14,650,719 17,894,429 21,856,305 größer Klassenobergrenze
Anteil
Abbildung A.86.: Modell LogLog, Er-gebnis D4, VaR
Wahrer Wert
0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000 8,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.87.: Modell LogLog, Er-gebnis D4, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
3,269,017 3,992,787 4,876,801 5,956,538 7,275,332 8,886,111 10,853,520 13,256,519 16,191,549 19,776,403 24,154,953 größer Klassenobergrenze
Anteil
Abbildung A.88.: Modell LogLog, Er-gebnis D4, ES
155
Zeile 5, λ=100
Wahrer Wert
9,200,000 9,300,000 9,400,000 9,500,000 9,600,000 9,700,000 9,800,000 9,900,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000
Iterationen
99.9% Quantil
Abbildung A.89.: Modell LogLog, Er-gebnis D5, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
6,582,993 7,275,332 8,040,485 8,886,111 9,820,671 10,853,520 11,994,995 13,256,519 14,650,719 16,191,549 17,894,429 größer Klassenobergrenze
Anteil
Abbildung A.90.: Modell LogLog, Er-gebnis D5, VaR
Wahrer Wert
9,400,000 9,600,000 9,800,000 10,000,000 10,200,000 10,400,000 10,600,000 10,800,000 11,000,000 11,200,000 11,400,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.91.: Modell LogLog, Er-gebnis D5, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
7,275,332 8,202,914 9,248,760 10,427,947 11,757,478 13,256,519 14,946,684 16,852,339 19,000,959 21,423,521 24,154,953 größer Klassenobergrenze
Anteil
Abbildung A.92.: Modell LogLog, Er-gebnis D5, ES
Zeile 6, λ=250
Wahrer Wert
18,600,000 18,800,000 19,000,000 19,200,000 19,400,000 19,600,000 19,800,000 20,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.93.: Modell LogLog, Er-gebnis D6, VaR, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
14,650,719 15,556,669 16,518,640 17,540,096 18,624,715 19,776,403 20,999,307 22,297,832 23,676,653 25,140,735 26,695,351 größer Klassenobergrenze
Anteil
Abbildung A.94.: Modell LogLog, Er-gebnis D6, VaR
Wahrer Wert
19,800,000 20,000,000 20,200,000 20,400,000 20,600,000 20,800,000 21,000,000
0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 900,000 1,000,000 Iterationen
99.9% Quantil
Abbildung A.95.: Modell LogLog, Er-gebnis D6, ES, Wahrer Wert
Histogramm
0%
5%
10%
15%
20%
25%
30%
16,191,549 17,365,569 18,624,715 19,975,159 21,423,521 22,976,902 24,642,915 26,429,728 28,346,100 30,401,424 32,605,776 größer Klassenobergrenze
Anteil
Abbildung A.96.: Modell LogLog, Er-gebnis D6, ES