TD
|
\(t_i\)
|
\(t_i\)
|
Price
|
TD
|
\(t_i\)
|
\(t_i\)
|
Price
|
TD
|
\(t_i\)
|
\(t_i \)
|
Price
|
---|
|
\((T=\frac{2}{12})\)
|
\((T=\frac{6}{12})\)
| | |
\((T=\frac{2}{12})\)
|
\((T=\frac{6}{12})\)
| | |
\((T=\frac{2}{12})\)
|
\((T=\frac{6}{12})\)
| |
---|
1/4
|
0
|
0
|
2.581
|
3/1
|
0
|
0.1545
|
2.777
|
5/3
|
0
|
0.3333
|
2.966
|
1/5
|
0.0045
|
0.0041
|
2.702
|
3/2
|
0.0039
|
0.1585
|
2.839
|
5/4
|
0.0041
|
0.3374
|
2.967
|
1/6
|
0.0090
|
0.0081
|
2.716
|
3/3
|
0.0078
|
0.1626
|
2.816
|
5/5
|
0.0081
|
0.3415
|
2.938
|
1/7
|
0.0135
|
0.0122
|
2.729
|
3/4
|
0.0116
|
0.1667
|
2.746
|
5/6
|
0.0122
|
0.3455
|
2.928
|
1/8
|
0.0180
|
0.0163
|
2.700
|
3/5
|
0.0155
|
0.1707
|
2.701
|
5/7
|
0.0163
|
0.3496
|
2.958
|
1/11
|
0.0225
|
0.0203
|
2.747
|
3/8
|
0.0194
|
0.1748
|
2.664
|
5/10
|
0.0203
|
0.3537
|
2.932
|
1/12
|
0.0270
|
0.0244
|
2.753
|
3/9
|
0.0233
|
0.1789
|
2.662
|
5/11
|
0.0244
|
0.3577
|
2.955
|
1/13
|
0.0315
|
0.0285
|
2.727
|
3/10
|
0.0271
|
0.1829
|
2.692
|
5/12
|
0.0285
|
0.3618
|
2.969
|
1/14
|
0.0360
|
0.0325
|
2.666
|
3/11
|
0.0310
|
0.1870
|
2.668
|
5/13
|
0.0325
|
0.3659
|
2.973
|
1/15
|
0.0405
|
0.0366
|
2.737
|
3/12
|
0.0349
|
0.1911
|
2.600
|
5/14
|
0.0366
|
0.3699
|
2.961
|
1/19
|
0.0450
|
0.0407
|
2.546
|
3/15
|
0.0388
|
0.1951
|
2.484
|
5/17
|
0.0407
|
0.3740
|
3.109
|
1/20
|
0.0495
|
0.0447
|
2.539
|
3/16
|
0.0426
|
0.1992
|
2.562
|
5/18
|
0.0447
|
0.3780
|
3.012
|
1/21
|
0.0541
|
0.0488
|
2.491
|
3/17
|
0.0465
|
0.2033
|
2.528
|
5/19
|
0.0488
|
0.3821
|
2.964
|
1/22
|
0.0586
|
0.0528
|
2.446
|
3/18
|
0.0504
|
0.2073
|
2.481
|
5/20
|
0.0528
|
0.3862
|
2.925
|
1/25
|
0.0631
|
0.0569
|
2.602
|
3/19
|
0.0543
|
0.2114
|
2.535
|
5/21
|
0.0569
|
0.3902
|
2.906
|
1/26
|
0.0676
|
0.0610
|
2.656
|
3/22
|
0.0581
|
0.2154
|
2.582
|
5/24
|
0.0610
|
0.3943
|
2.886
|
1/27
|
0.0721
|
0.0650
|
2.760
|
3/23
|
0.0620
|
0.2195
|
2.508
|
5/25
|
0.0650
|
0.3984
|
2.913
|
1/28
|
0.0766
|
0.0691
|
2.664
|
3/24
|
0.0659
|
0.2236
|
2.518
|
5/26
|
0.0691
|
0.4024
|
2.984
|
1/29
|
0.0811
|
0.0732
|
2.564
|
3/25
|
0.0698
|
0.2276
|
2.570
|
5/27
|
0.0732
|
0.4065
|
2.958
|
2/1
|
0.0856
|
0.0772
|
2.850
|
3/26
|
0.0736
|
0.2317
|
2.557
|
5/28
|
0.0772
|
0.4106
|
2.986
|
2/2
|
0.0901
|
0.0813
|
2.845
|
3/29
|
0.0775
|
0.2358
|
2.586
|
6/1
|
0.0813
|
0.4146
|
3.104
|
2/3
|
0.0956
|
0.0854
|
2.789
|
3/30
|
0.0814
|
0.2398
|
2.623
|
6/2
|
0.0854
|
0.4187
|
3.075
|
2/4
|
0.0991
|
0.0894
|
2.935
|
3/31
|
0.0853
|
0.2439
|
2.608
|
6/3
|
0.0894
|
0.4228
|
3.041
|
2/5
|
0.1036
|
0.0935
|
2.863
|
4/1
|
0.0891
|
0.2480
|
2.639
|
6/4
|
0.0935
|
0.4268
|
3.097
|
2/8
|
0.1081
|
0.0976
|
2.882
|
4/5
|
0.0930
|
0.2520
|
2.511
|
6/7
|
0.0976
|
0.4309
|
3.070
|
2/9
|
0.1126
|
0.1016
|
2.835
|
4/6
|
0.0969
|
0.2561
|
2.456
|
6/8
|
0.1016
|
0.4350
|
3.128
|
2/10
|
0.1171
|
0.1057
|
2.911
|
4/7
|
0.1008
|
0.2602
|
2.520
|
6/9
|
0.1057
|
0.4390
|
3.129
|
2/11
|
0.1216
|
0.1098
|
2.868
|
4/8
|
0.1047
|
0.2642
|
2.522
|
6/10
|
0.1098
|
0.4431
|
3.149
|
2/12
|
0.1261
|
0.1138
|
2.912
|
4/9
|
0.1085
|
0.2683
|
2.526
|
6/11
|
0.1138
|
0.4472
|
3.296
|
2/16
|
0.1306
|
0.1179
|
3.129
|
4/12
|
0.1124
|
0.2724
|
2.561
|
6/14
|
0.1179
|
0.4512
|
3.325
|
2/17
|
0.1351
|
0.1220
|
3.219
|
4/13
|
0.1163
|
0.2764
|
2.619
|
6/15
|
0.1220
|
0.4553
|
3.240
|
2/18
|
0.1396
|
0.1260
|
3.082
|
4/14
|
0.1202
|
0.2805
|
2.618
|
6/16
|
0.1260
|
0.4593
|
3.251
|
2/19
|
0.1441
|
0.1301
|
3.069
|
4/15
|
0.1240
|
0.2846
|
2.658
|
6/17
|
0.1301
|
0.4634
|
3.253
|
2/22
|
0.1486
|
0.1341
|
2.953
|
4/16
|
0.1279
|
0.2886
|
2.680
|
6/18
|
0.1341
|
0.4675
|
3.215
|
2/23
|
0.1532
|
0.1382
|
2.879
|
4/19
|
0.1318
|
0.2927
|
2.749
|
6/21
|
0.1382
|
0.4715
|
3.191
|
2/24
|
0.1577
|
0.1423
|
2.854
|
4/20
|
0.1357
|
0.2967
|
2.727
|
6/22
|
0.1423
|
0.4756
|
3.258
|
2/25
|
0.1622
|
0.1463
|
2.777
|
4/21
|
0.1395
|
0.3008
|
2.692
|
6/23
|
0.1463
|
0.4797
|
3.333
|
2/26
|
0.1667
|
0.1504
|
2.771
|
4/22
|
0.1434
|
0.3049
|
2.749
|
6/24
|
0.1504
|
0.4837
|
3.418
|
| | | |
4/23
|
0.1473
|
0.3089
|
2.730
|
6/25
|
0.1545
|
0.4878
|
3.496
|
| | | |
4/26
|
0.1512
|
0.3130
|
2.790
|
6/28
|
0.1585
|
0.4919
|
3.617
|
| | | |
4/27
|
0.1550
|
0.3171
|
2.873
|
6/29
|
0.1626
|
0.4959
|
3.630
|
| | | |
4/28
|
0.1589
|
0.3211
|
2.925
|
6/30
|
0.1667
|
0.5000
|
3.650
|
| | | |
4/29
|
0.1628
|
0.3252
|
2.911
| | | | |
| | | |
4/30
|
0.1667
|
0.3293
|
2.931
| | | | |
- Here, \(t_i\) is the ith trading day (TD), such that \(t_i=\frac{T}{n-1}\times i\), for \(i=0,\ldots ,n-1\)