The quadratic approximation of Barone-Adesi and Whaley writes the American value as the European value plus a premium of the form , where the exponent solves the quadratic that the time-independent part of the pricing equation imposes, and the critical spot is found numerically from value matching and smooth pasting at . Beyond the option is worth its exercise value.
| spot | expiry | rate | yield | European | tree (2 001) | quadratic | error |
|---|---|---|---|---|---|---|---|
| 100 | 1 | 5% | 0 | 5.5735 | 6.0902 | 6.0976 | |
| 90 | 0.5 | 8% | 0 | 11.2671 | 12.1792 | 12.1151 | |
| 110 | 0.25 | 3% | 0 | 1.5070 | 1.5201 | 1.5229 | |
| 100 | 1 | 5% | 4% | 9.0396 | 9.2168 | 9.2444 |