lognormalPart3

LognormalPart3

Current Price (S)
40
Strike Price (X)
100
Volatility
20%
Expected return
8.00%
Term
3
Standardized LN(S)
 0.40 
P(future S < X)
65%
P(future S > X)
35%
Z
#N/A
-3.0
 0.0044 
 0.0013 
 0.00 
-2.9
 0.0060 
 0.0019 
 0.01 
-2.8
 0.0079 
 0.0026 
 0.01 
-2.7
 0.0104 
 0.0035 
 0.01 
-2.6
 0.0136 
 0.0047 
 0.01 
-2.5
 0.0175 
 0.0062 
 0.02 
-2.4
 0.0224 
 0.0082 
 0.02 
-2.3
 0.0283 
 0.0107 
 0.03 
-2.2
 0.0355 
 0.0139 
 0.04 
-2.1
 0.0440 
 0.0179 
 0.04 
-2.0
 0.0540 
 0.0228 
 0.05 
-1.9
 0.0656 
 0.0287 
 0.07 
-1.8
 0.0790 
 0.0359 
 0.08 
-1.7
 0.0940 
 0.0446 
 0.09 
-1.6
 0.1109 
 0.0548 
 0.11 
-1.5
 0.1295 
 0.0668 
 0.13 
-1.4
 0.1497 
 0.0808 
 0.15 
-1.3
 0.1714 
 0.0968 
 0.17 
-1.2
 0.1942 
 0.1151 
 0.19 
-1.1
 0.2179 
 0.1357 
 0.22 
-1.0
 0.2420 
 0.1587 
 0.24 
-0.9
 0.2661 
 0.1841 
 0.27 
-0.8
 0.2897 
 0.2119 
 0.29 
-0.7
 0.3123 
 0.2420 
 0.31 
-0.6
 0.3332 
 0.2743 
 0.33 
-0.5
 0.3521 
 0.3085 
 0.35 
-0.4
 0.3683 
 0.3446 
 0.37 
-0.3
 0.3814 
 0.3821 
 0.38 
-0.2
 0.3910 
 0.4207 
 0.39 
-0.1
 0.3970 
 0.4602 
 0.40 
0.0
 0.3989 
 0.5000 
 0.40 
0.1
 0.3970 
 0.5398 
 0.40 
0.2
 0.3910 
 0.5793 
 0.39 
0.3
 0.3814 
 0.6179 
 0.38 
0.4
 0.3683 
 0.6554 
  
0.5
 0.3521 
 0.6915 
  
0.6
 0.3332 
 0.7257 
  
0.7
 0.3123 
 0.7580 
  
0.8
 0.2897 
 0.7881 
  
0.9
 0.2661 
 0.8159 
  
1.0
 0.2420 
 0.8413 
  
1.1
 0.2179 
 0.8643 
  
1.2
 0.1942 
 0.8849 
  
1.3
 0.1714 
 0.9032 
  
1.4
 0.1497 
 0.9192 
  
1.5
 0.1295 
 0.9332 
  
1.6
 0.1109 
 0.9452 
  
1.7
 0.0940 
 0.9554 
  
1.8
 0.0790 
 0.9641 
  
1.9
 0.0656 
 0.9713 
  
2.0
 0.0540 
 0.9772 
  
2.1
 0.0440 
 0.9821 
  
2.2
 0.0355 
 0.9861 
  
2.3
 0.0283 
 0.9893 
  
2.4
 0.0224 
 0.9918 
  
2.5
 0.0175 
 0.9938 
  
2.6
 0.0136 
 0.9953 
  
2.7
 0.0104 
 0.9965 
  
2.8
 0.0079 
 0.9974 
  
2.9
 0.0060 
 0.9981 
  
3.0
 0.0044 
 0.9987 
  

Lognormal

Lognormal distribution
Mean
0
Standard deviation
1
Bond Price: zero-coupon bond
Par value
100
Interest rate:
mean
7%
Standard Dev
3%
Term
20
Lognormal
Z
#N/A
pdf
CDF
yield
Price
-3.0
 0.0044 
-2.00%
149.182469764129
-2.9
 0.0060 
-1.70%
140.494759056361
-2.8
 0.0079 
-1.40%
132.312981233745
-2.7
 0.0104 
-1.10%
124.60767305874
-2.6
 0.0136 
-0.80%
117.351087099183
-2.5
 0.0175 
-0.50%
110.517091807566
-2.4
 0.0224 
-0.20%
104.08107741924
-2.3
 0.0283 
0.10%
98.0198673306768
-2.2
 0.0355 
0.40%
92.3116346386648
-2.1
 0.0440 
0.70%
86.9358235398817
-2.0
 0.0540 
1.00%
81.8730753077992
-1.9
 0.0656 
1.30%
77.1051585803576
-1.8
 0.0790 
1.60%
72.61490370737
-1.7
 0.0940 
1.90%
68.3861409212364
-1.6
 0.1109 
2.20%
64.4036421083149
-1.5
 0.1295 
2.50%
60.6530659712641
-1.4
 0.1497 
2.80%
57.1209063848822
-1.3
 0.1714 
3.10%
53.7944437594681
-1.2
 0.1942 
3.40%
50.6616992365596
-1.1
 0.2179 
3.70%
47.711391552104
-1.0
 0.2420 
4.00%
44.9328964117227
-0.9
 0.2661 
4.30%
42.3162082317754
-0.8
 0.2897 
4.60%
39.8519041084519
-0.7
 0.3123 
4.90%
37.5311098851404
-0.6
 0.3332 
5.20%
35.3454681958784
-0.5
 0.3521 
5.50%
33.2871083698084
-0.4
 0.3683 
5.80%
31.3486180882609
-0.3
 0.3814 
6.10%
29.5230166924018
-0.2
 0.3910 
6.40%
27.8037300453198
-0.1
 0.3970 
6.70%
26.1845668580329
0.0
 0.3989 
0
7.00%
24.6596963941609
0.1
 0.3970 
0.28159018901519
0.01065109934169
7.30%
23.2236274729762
0.2
 0.3910 
0.54626787075815
0.05376031045165
7.60%
21.8711886952217
0.3
 0.3814 
0.64420325735919
0.11430004504914
7.90%
20.5975098204886
0.4
 0.3683 
0.65544416806031
0.17975721389577
8.20%
19.3980042290894
0.5
 0.3521 
0.62749607711593
0.24410859578557
8.50%
18.2683524052737
0.6
 0.3332 
0.58357382259451
0.30473658251022
8.80%
17.2044863823053
0.7
 0.3123 
0.53479483207693
0.36066758262264
9.10%
16.2025750933883
0.8
 0.2897 
0.48641578111156
0.41171189185744
9.40%
15.2590105756886
0.9
 0.2661 
0.44081568591204
0.45804487278565
9.70%
14.3703949777705
1.0
 0.2420 
0.39894228040144
0.49999999999999
10.00%
13.5335283236614
1.1
 0.2179 
0.36103126122905
0.53796577142461
10.30%
12.7453969894822
1.2
 0.1942 
0.32697202407426
0.57233480883676
10.60%
12.0031628511458
1.3
 0.1714 
0.29649637063611
0.60347968963215
10.90%
11.3041530640451
1.4
 0.1497 
0.26927622894994
0.63174260783667
11.20%
10.6458504379254
1.5
 0.1295 
0.24497365171051
0.65743216948515
11.50%
10.0258843722805
1.6
 0.1109 
0.2232654474303
0.68082378767482
11.80%
9.44202231963034
1.7
 0.0940 
0.20385425949788
0.70216179269914
12.10%
8.89216174593874
1.8
 0.0790 
0.18647244853891
0.72166225206508
12.40%
8.37432255921969
1.9
 0.0656 
0.17088223824122
0.7395159710347
12.70%
7.88663997906758
2.0
 0.0540 
0.15687401927898
0.75589140421441
13.00%
7.42735782143347
2.1
 0.0440 
0.14426384634321
0.77093735097544
13.30%
6.99482217446562
2.2
 0.0355 
0.13289068604819
0.78478538481714
13.60%
6.58747544264037
2.3
 0.0283 
0.12261370693199
0.79755200795048
13.90%
6.20385073773591
2.4
 0.0224 
0.11330975388971
0.80934054333511
14.20%
5.84256659645015
2.5
 0.0175 
0.10487106688965
0.82024278610421
14.50%
5.50232200564079
2.6
 0.0136 
0.09720325902429
0.83034043982357
14.80%
5.18189171727264
2.7
 0.0104 
0.0902235455797
0.83970636323641
15.10%
4.88012183620135
2.8
 0.0079 
0.08385920456949
0.84840565167733
15.40%
4.59592566490447
2.9
 0.0060 
0.07804624472163
0.85649657511962
15.70%
4.32827979019664
3.0
 0.0044 
0.07272825614
0.86403139235857
16.00%
4.07622039783667