方差gamma下美式期权的快速定价方法

CPU是平均计算时间。σνθK FD fine fdrough main simple0.10 0.10-0.50 2800 26.961 27.062 27.040 26.882 26.4790.40 0.60-0.50 2800 80.429 80.563 80.484 79.724 81.2410.10 0.60-0.10 2800 12.088 12.114 12.596 11.976 11.9270.40 0.10-0.10 2800 71.324 71.735 71.317 72.177 71.4510 0.10-0.50 2900 53.119 53.372 53.191 52.564 52.2480.40 0.60-0.50 2900 100.103 100.741 100.121 98.937 101.7650.10 0.60-0.102900 24.642 23.303 24.863 24.880 24.6800.40 0.10-0.10 2900 110.992 111.634 110.895 110.727 111.2510.10 0.10-0.50 3000 104.401 104.780 104.275 103.621 102.5070.40 0.60-0.50 3000 130.478 132.460 130.763 129.990 132.7380.10 0 0 0.60-0.10 3000 99 99 99 99.990 100.000 100.000 96.1030.40 0 0.10-0.10 3000 170.431 170.888 170.459 170.141 171.060RMSE-0.772 0.189 0.575 1.549MAE-1.982 0.508 1.165 3.896CPU（s） 5.085 0.129 0.010 5.340 0.017表2：美式看跌期权的价值。S=2900，T=1/12，r=0.05，q=0.01。RMSE是均方误差的根。MAE是最大绝对误差。

CPU是平均计算时间。σνθK FD fine fdrough main simple0.10 0.10-0.50 2800 59.653 59.862 59.513 59.787 57.9200.40 0.60-0.50 2800 185.871 186.004 186.024 187.613 188.5290.10 0.60-0.10 2800 30.065 30.105 30.303 29.745 29.1880.40 0 0 0.10-0.10 2800 158.556 159.291 158.513 157.752 158.9270.10 0-0.10 50 2900 94.364 94.800 94.134 93.273 91.7720.40 0.60-0.50 2900 218.131 218.341 218.325 219.145 222.4960.100.60-0.10 2900 52.210 52.428 52.392 51.713 51.3980.40 0.10-0.10 2900 205.451 206.251 205.350 203.691 206.0400.10 0.10-0.50 3000 143.833 144.524 143.769 142.954 140.1620.40 0.60-0.50 3000 255.864 256.189 256.130 255.742 262.5320.10 0.60-0.10 3000 99.999 100.454 100.000 100.000 95.9360 0.10-0.10 0.10 3000 260.438 261.227 260.350 260.751 261.350RMSE-0.495 0.163 0.924 3.069MAE-0.800 0.2651.760 6.668CPU 5.161 0.126 0.009 5.567 0.007表3：美式看跌期权的价值。S=2900，T=1/4，r=0.05，q=0.01。RMSE是均方误差的根。MAE是最大绝对误差。

CPU是平均计算时间。σνθK FD fine fdrough main simple0.10 0.10-0.50 2700 99.153 99.283 98.397 98.443 95.1050.40 0.60-0.50 2700 388.210 388.464 388.304 386.251 393.8370.10 0.60-0.10 2700 51.101 51.065 50.808 50.683 47.2270.40 0 0 0 0.10-0.10 2700 299 299.414 300.591 299.140 299.877 299.3720.10 0.10 10-0.50 2900 173.557 174.300 171.605 171.854 166.9930.40 0.60-0.50 2900 477.476 478.033 477.634 476.004489.7160.10 0.60-0.10 2900 106.615 106.757 106.492 105.221 101.4730.40 0.10-0.10 2900 398.183 399.491 397.314 395.952 398.1540.10 0.10-0.50 3100 279.825 281.131 277.009 277.950 270.7150.40 0.60-0.50 3100 578.029 578.940 578.297 580.304 599 7340.10 0.60-0.10 3100 208.763 209.230 208.261 205.385 203.5100.40 0.10-0.10 3100 511.520 512.885 509.924 511.852 511.607RMSE-0.850 1.160 1.7548.486MAE-1.365 2.816 3.378 21.705CPU（s）5.130 0.125 0.010 5.758 0.004表4：美国看跌期权的价值。S=2900，T=1，r=0.05，q=0.01。RMSE是均方误差的根。MAE是最大绝对误差。CPU是平均计算时间。