Table 1 Accuracy across different moneyness \(\frac{K}{S_0}\) and maturity T
From: A closed-form pricing formula for European options in an illiquid asset market
\({{\mathbf{K }/\mathbf{S }_\mathbf{0 }}}\) | 0.8 | 0.85 | 0.9 | 0.95 | 1 | 1.05 | 1.10 | 1.15 | 1.2 |
|---|---|---|---|---|---|---|---|---|---|
T=0.25 | Â | ||||||||
Authors | 20.6059 | 16.1565 | 12.1767 | 8.8290 | 6.1928 | 4.2411 | 2.8668 | 1.9320 | 1.3080 |
MC | 20.6508 | 16.2002 | 12.2146 | 8.8611 | 6.2203 | 4.2620 | 2.8808 | 1.9399 | 1.3129 |
(±0.0512) | (±0.0491) | (±0.0459) | (±0.0417) | (±0.0369) | (±0.0319) | (±0.0273) | (±0.0231) | (±0.0196) | |
RE(%) | 0.22 | 0.27 | 0.31 | 0.36 | 0.44 | 0.49 | 0.49 | 0.41 | 0.37 |
T=0.5 | Â | ||||||||
Authors | 22.2044 | 18.3607 | 14.9632 | 12.0507 | 9.6242 | 7.6515 | 6.0782 | 4.8400 | 3.8730 |
MC | 22.2811 | 18.4308 | 15.0273 | 12.1090 | 9.6764 | 7.6946 | 6.1107 | 4.8656 | 3.8936 |
(±0.0797) | (±0.0765) | (±0.0727) | (± 0.0684) | (±0.0638) | (±0.0593) | (±0.0548) | (±0.0506) | (±0.0467) | |
RE(%) | 0.34 | 0.38 | 0.43 | 0.48 | 0.54 | 0.56 | 0.53 | 0.53 | 0.53 |
T=0.75 | Â | ||||||||
Authors | 24.1643 | 20.7209 | 17.6618 | 14.9924 | 12.6991 | 10.7540 | 9.1204 | 7.7576 | 6.6250 |
MC | 24.1316 | 20.6906 | 17.6294 | 14.9573 | 12.6628 | 10.7156 | 9.0800 | 7.7148 | 6.5795 |
(±0.1087) | (±0.1052) | (± 0.1014) | (±0.0973) | (±0.0930) | (±0.0888) | (±0.0846) | (±0.0806) | (±0.0768) | |
RE(%) | 0.14 | 0.15 | 0.18 | 0.23 | 0.29 | 0.36 | 0.45 | 0.55 | 0.69 |
T=1 | Â | ||||||||
Authors | 26.2393 | 23.0847 | 20.2625 | 17.7660 | 15.5784 | 13.6760 | 12.0308 | 10.6132 | 9.3941 |
MC | 26.2718 | 23.1155 | 20.2886 | 17.7896 | 15.5999 | 13.6973 | 12.0514 | 10.6347 | 9.4163 |
(±0.1442) | (±0.1408) | (±0.1371) | (±0.1333) | (±0.1295) | (±0.1256) | (±0.1218) | (±0.1181) | (±0.1146) | |
RE(%) | 0.12 | 0.13 | 0.13 | 0.13 | 0.14 | 0.16 | 0.17 | 0.20 | 0.24 |