Options Pricing With Bs & Binomial Trees
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S ($) K ($) r (%) δ (%) σ (%) T (ans) N Option Price
40 40 8% 6% 30% 1 20
type d'option Européenne
2
Américaine
genre d'option Call ●
Put
Δ Γ θ (journalier) vega(par pourcent*) ρ(par pourcent*) Ψ(par pourcent*) Ω
* On entend par "par pourcent" , le changement dans le prix de l'option par pourcent de changement dans le paramètre var
2
le changement dans le prix ngement dans le paramètre variable
Stock's tree
73.82 68.96 64.42 60.18 56.22 52.52 49.06 45.83 42.82 40
49.16
42.9 40.08
37.44
49.26
42.99
37.52
43.08
37.59
32.81
43.16 40.32
37.67 35.19
32.87 30.71
49.36 46.11
40.24
35.12
56.45 52.73
46.02
40.16
35.05
60.3 56.33
52.63
45.93
64.55
37.74 35.26
32.94 30.77
28.75
33 30.83
28.8 26.91
28.86 26.96
25.19
25.24 23.58 22.07
Option's tree
0 0.02 0.07 0.2 0.44 0.82 1.39 2.15 3.1 4.23
1.19
2.87 4.01
5.32
0.99
2.63
5.11
2.37
4.88
8.01
2.09 3.25
4.63 6.18
7.85 9.59
0.78 1.45
3.53
6.39
0.21 0.5
1.7
3.78
6.58
0.32 0.66
1.93
0.04 0.13
4.36 5.96
7.68 9.46
11.29
7.5 9.34
11.21 13.09
11.14 13.04
14.81
14.76 16.42 17.93
Valeur de l'option =
4.23
145.83 136.23 127.27 118.89 111.06 103.75 96.93 90.55 84.59 79.02 73.97 69.1 64.68 60.54
52.84 49.46 46.2 43.25 40.4 37.82 33.07 30.89 28.92 27.01 25.29 23.62 22.11 20.66 19.34
25.44
22.2
19.37
22.25
19.41
16.94
22.29 20.82
19.45 18.17
16.98 15.86
25.49 23.81
20.78
18.14
29.15 27.23
23.77
20.74
18.1
29.09
25.39
22.16
33.34 31.14
27.18
23.72
20.7
33.27
29.03
25.34
38.12 35.61
31.08
27.12
23.67
38.05
33.2
28.98 27.07
43.6 40.73
35.54
31.02
49.86 46.57
43.51
37.97
33.14 30.96
49.76
40.65
35.47
57.01 53.26
46.48 43.42
37.89 35.4
60.91
53.15
40.56
65.2
56.9
49.66
43.34 40.48
35.33
60.79
46.39
74.56 69.65
65.07
56.79
49.56 46.3
74.41
64.94
53.05
85.27 79.65
69.51
60.67
52.94
85.1
74.26
56.67
97.51 91.09
79.5
69.38 64.81
56.56
97.31
84.93
74.11
111.51 104.17
90.91
79.34
69.24
60.42
97.12
84.76 79.18
111.29 103.96
90.73
127.52 119.13
19.49 18.21
17.01 15.89
14.84
17.04 15.92
14.87 13.9
14.9 13.92
13.01
13.03 12.18 11.4
0 0 0 0 0 0 0 0 0
0
0 0
0 0
0 0
0 0
0
0 0
0 0
0
0
0
0 0
0.01
0 0
0 0.01
0.06
0
0.11 0.57 1.79 2.95 4.07 5.72 7.31 9.22
9.1
12.99 14.71 16.38 17.89 19.34
14.56 17.75
20.59
23.06
17.71 19.18
20.55 21.83
23.02 24.14
14.51 16.19
19.22
21.86
10.85 12.77
16.23 17.8
20.63 21.9
8.86
12.82
19.26
6.66
10.91
14.61
17.84 19.3
20.66
8.92
16.28
2.22 4.5
6.73
10.97
14.66 16.33
2.87
6.92
12.88
0 1.14
4.84
8.98
12.93
0.59
3.34
11.02
0 0
1.76
5.17 7.11
11.08
0
1.05
3.73
0 0
0.3
2.22
5.46
0
0.16
1.44
0 0
0
0.62
2.61
0
0
0.36
0 0
0
0.08
0.91
0
0
0.04
0
0
0
0.2
1.19
0 0
0.02
0.35
0
20.51 21.79
22.99 24.11
25.16
22.96 24.08
25.13 26.1
25.1 26.08
26.99
26.97 27.82 28.6
156.1 136.5 119.37 104.38 91.27 79.81 69.79 61.03 53.37 46.67 40.81 35.68 31.2 27.29 23.86 20.86 18.25 15.95 13.95 12.2 10.67 0 0 0 0 0
0 0 0 0 0 0 4.32 8.8 12.71 16.14 19.14 21.75 24.05 26.05 27.8 29.33
40 40 8% 6% 30% 1 20
type d'option Européenne
2
Américaine
genre d'option Call ●
Put
Δ Γ θ (journalier) vega(par pourcent*) ρ(par pourcent*) Ψ(par pourcent*) Ω
* On entend par "par pourcent" , le changement dans le prix de l'option par pourcent de changement dans le paramètre var
2
le changement dans le prix ngement dans le paramètre variable
Stock's tree
73.82 68.96 64.42 60.18 56.22 52.52 49.06 45.83 42.82 40
49.16
42.9 40.08
37.44
49.26
42.99
37.52
43.08
37.59
32.81
43.16 40.32
37.67 35.19
32.87 30.71
49.36 46.11
40.24
35.12
56.45 52.73
46.02
40.16
35.05
60.3 56.33
52.63
45.93
64.55
37.74 35.26
32.94 30.77
28.75
33 30.83
28.8 26.91
28.86 26.96
25.19
25.24 23.58 22.07
Option's tree
0 0.02 0.07 0.2 0.44 0.82 1.39 2.15 3.1 4.23
1.19
2.87 4.01
5.32
0.99
2.63
5.11
2.37
4.88
8.01
2.09 3.25
4.63 6.18
7.85 9.59
0.78 1.45
3.53
6.39
0.21 0.5
1.7
3.78
6.58
0.32 0.66
1.93
0.04 0.13
4.36 5.96
7.68 9.46
11.29
7.5 9.34
11.21 13.09
11.14 13.04
14.81
14.76 16.42 17.93
Valeur de l'option =
4.23
145.83 136.23 127.27 118.89 111.06 103.75 96.93 90.55 84.59 79.02 73.97 69.1 64.68 60.54
52.84 49.46 46.2 43.25 40.4 37.82 33.07 30.89 28.92 27.01 25.29 23.62 22.11 20.66 19.34
25.44
22.2
19.37
22.25
19.41
16.94
22.29 20.82
19.45 18.17
16.98 15.86
25.49 23.81
20.78
18.14
29.15 27.23
23.77
20.74
18.1
29.09
25.39
22.16
33.34 31.14
27.18
23.72
20.7
33.27
29.03
25.34
38.12 35.61
31.08
27.12
23.67
38.05
33.2
28.98 27.07
43.6 40.73
35.54
31.02
49.86 46.57
43.51
37.97
33.14 30.96
49.76
40.65
35.47
57.01 53.26
46.48 43.42
37.89 35.4
60.91
53.15
40.56
65.2
56.9
49.66
43.34 40.48
35.33
60.79
46.39
74.56 69.65
65.07
56.79
49.56 46.3
74.41
64.94
53.05
85.27 79.65
69.51
60.67
52.94
85.1
74.26
56.67
97.51 91.09
79.5
69.38 64.81
56.56
97.31
84.93
74.11
111.51 104.17
90.91
79.34
69.24
60.42
97.12
84.76 79.18
111.29 103.96
90.73
127.52 119.13
19.49 18.21
17.01 15.89
14.84
17.04 15.92
14.87 13.9
14.9 13.92
13.01
13.03 12.18 11.4
0 0 0 0 0 0 0 0 0
0
0 0
0 0
0 0
0 0
0
0 0
0 0
0
0
0
0 0
0.01
0 0
0 0.01
0.06
0
0.11 0.57 1.79 2.95 4.07 5.72 7.31 9.22
9.1
12.99 14.71 16.38 17.89 19.34
14.56 17.75
20.59
23.06
17.71 19.18
20.55 21.83
23.02 24.14
14.51 16.19
19.22
21.86
10.85 12.77
16.23 17.8
20.63 21.9
8.86
12.82
19.26
6.66
10.91
14.61
17.84 19.3
20.66
8.92
16.28
2.22 4.5
6.73
10.97
14.66 16.33
2.87
6.92
12.88
0 1.14
4.84
8.98
12.93
0.59
3.34
11.02
0 0
1.76
5.17 7.11
11.08
0
1.05
3.73
0 0
0.3
2.22
5.46
0
0.16
1.44
0 0
0
0.62
2.61
0
0
0.36
0 0
0
0.08
0.91
0
0
0.04
0
0
0
0.2
1.19
0 0
0.02
0.35
0
20.51 21.79
22.99 24.11
25.16
22.96 24.08
25.13 26.1
25.1 26.08
26.99
26.97 27.82 28.6
156.1 136.5 119.37 104.38 91.27 79.81 69.79 61.03 53.37 46.67 40.81 35.68 31.2 27.29 23.86 20.86 18.25 15.95 13.95 12.2 10.67 0 0 0 0 0
0 0 0 0 0 0 4.32 8.8 12.71 16.14 19.14 21.75 24.05 26.05 27.8 29.33
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