Research Article
Polynomial Chaos Expansion Approach to Interest Rate Models
Table 14
Errors of average and variance computed by MC and QMC methods for the GBM evaluated at time
, with parameters
,
, and
.
| | Size of sampling | Average | Variance | | | | |
| | 256 | 9.3149e − 01 | 1.7295e − 01 | 1.9672e + 01 | 6.5079e + 00 | | 512 | 6.7405e − 01 | 9.4193e − 02 | 1.4553e + 01 | 3.6819e + 00 | | 1024 | 4.8747e − 01 | 5.0744e − 02 | 1.0759e + 01 | 2.0760e + 00 | | 2048 | 3.3705e − 01 | 2.7110e − 02 | 7.2722e + 00 | 1.1656e + 00 | | 4096 | 2.3915e − 01 | 1.4388e − 02 | 5.1771e + 00 | 6.5155e − 01 | | 8192 | 1.7213e − 01 | 7.5954e − 03 | 3.7926e + 00 | 3.6254e − 01 | | 16384 | 1.2203e − 01 | 3.9921e − 03 | 2.6956e + 00 | 2.0082e − 01 | | 32768 | 8.6400e − 02 | 2.0905e − 03 | 1.9111e + 00 | 1.1076e − 01 | | 65536 | 6.0926e − 02 | 1.0913e − 03 | 1.3439e + 00 | 6.0845e − 02 |
|
|
