Pricing American Options Using a Nonparametric Entropy Approach
Table 6
MPE, MSE, and MAPE of IBM put price estimates compared to IBM market prices for a range of moneyness and time to expiration.
Moneyness
Expiration
16–60 (short)
61–160 (medium)
161–357 (long)
Method
RMEL
Liu10
AA10
FD
RMEL
Liu10
AA10
FD
RMEL
Liu10
AA10
FD
(DOTM)
Count
372
618
374
MPE (%)
−46.223
−78.924
−82.536
−88.694
−30.291
−53.189
−51.623
−89.083
−4.054
0.899
−40.284
−75.498
MSE
0.057
0.439
1.206
0.634
0.115
0.754
2.064
1.945
0.826
2.397
2.203
3.219
MAPE (%)
49.451
79.437
82.735
96.226
36.683
60.518
59.137
89.083
24.695
47.858
45.735
75.498
(OTM)
Count
351
299
241
MPE (%)
−2.021
−15.641
−21.253
−28.855
−0.688
4.292
−5.382
−28.834
−0.183
9.063
−8.15
−24.484
MSE
0.127
1.150
1.851
2.526
0.521
2.712
2.685
4.631
5.193
11.681
5.346
5.218
MAPE (%)
10.390
37.253
37.564
48.761
11.254
33.690
30.258
31.554
24.518
46.614
25.458
24.711
(ITM)
Count
331
262
254
MPE (%)
0.389
0.817
−3.358
9.457
−0.960
−4.337
−1.861
−1.856
−7.996
−9.825
−7.658
−4.303
MSE
0.202
0.405
1.513
3.625
0.328
1.928
2.358
3.182
2.748
7.835
5.865
3.856
MAPE (%)
3.336
5.780
5.632
17.023
3.470
9.756
5.861
12.354
9.309
18.275
10.843
10.473
(DITM)
Count
239
523
566
MPE (%)
−0.566
−0.571
−0.865
5.747
−0.662
−1.706
−0.952
2.997
−2.372
−3.535
−2.536
2.041
MSE
0.226
0.172
1.263
2.547
0.489
0.727
1.213
1.924
1.118
2.098
2.253
2.040
MAPE (%)
1.589
1.822
1.832
5.899
1.845
2.250
1.925
3.928
2.623
3.811
3.531
3.624
Note: each reported value is for a particular combination of moneyness and time to expiration. Three independent simulations are carried out, while 10,000 underlying price paths are generated in each simulation. The first row reports the number of put options with the corresponding combination of moneyness and time to expiration. The remaining rows show the statistic results of the MPE, RMSE, and MAPE for each combination. The total number of options analyzed is 4430, the lowest moneyness is , the highest moneyness is , and the time to expiration is in between 16 and 357 days.
