Pricing American Options Using a Nonparametric Entropy Approach
Table 5
MPE, MSE, and MAPE of IBM call 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
RMEL
Liu10
AA10
RMEL
Liu10
AA10
(DOTM)
Count
199
480
529
MPE (%)
−5.352
−14.208
6.214
−3.508
−3.931
−7.035
−6.035
−7.932
−12.136
MSE
1.823
5.636
1.402
1.489
4.785
2.902
1.806
4.757
6.238
MAPE (%)
14.735
26.291
21.035
15.225
35.138
20.186
15.132
32.248
17.301
(OTM)
Count
371
304
290
MPE (%)
−5.130
2.620
5.326
−4.919
−4.634
−18.325
−5.726
−4.482
−20.648
MSE
1.290
4.064
1.824
1.164
4.060
3.028
1.357
4.814
4.039
MAPE (%)
19.868
44.545
23.894
16.825
35.937
27.682
19.781
42.443
26.026
(ITM)
Count
289
248
202
MPE (%)
−3.044
−2.307
−6.563
−4.688
−2.794
−19.542
−0.831
1.652
−23.249
MSE
1.314
3.906
3.358
0.873
3.046
8.065
1.106
3.495
16.548
MAPE (%)
17.060
34.599
18.175
18.988
38.985
25.338
20.091
41.227
28.065
(DITM)
Count
434
670
414
MPE (%)
−2.181
−3.637
−4.212
−2.846
−7.860
−9.542
−5.096
−8.887
−11.254
MSE
1.386
4.290
2.921
1.189
3.915
8.621
0.725
3.085
15.245
MAPE (%)
15.663
37.031
13.984
15.690
31.904
15.938
18.616
38.707
19.351
Note: each cell represents 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 call 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 analysed is 4430, the lowest moneyness is , the highest moneyness is , and the time to expiration is in between 16 and 357 days.
