Sheet1
Heston two-factor model
rho 12 -0.9 Z eps 1 eps 2
dt 0.5 0.1212719 0.2952849
mu 0.1 0.1472987 0.40124017
k 1.8 -1.82467762 0.24039157
theta 0.25 2.17774812 -0.07341225
sigma 0.12 0.20236921 -0.2434211
S0 1 Y=LZ dW1 dW2
V0 0.01 0.0857521829 0.013835954
0.1041559096 0.0299302075
Cholesky Factor Matrix L -1.2902419186 1.2353113847
0.7071067812 0 1.5399004634 -1.4085375921
-0.6363961031 0.3082207001 0.1430966407 -0.2038143985
dV2 V2 dS2 S2
0.0081623566 0.2509378654 0.0912310848 1.0801641291
0.0261162804 0.2510888854 0.1058296666 1.1704878982
0.0097933683 0.4136200326 -0.7090727619 0.2119030463
-0.1251023964 0.076095254 0.7870709534 1.8496417684
-0.3537659503 0.2621320747 0.1187393006 0.8503383597
Ave 1.0325070403
STD 0.5906766083
std error 0.2641586098 ！ Note : need to change sqrt(n)
dV1 V1 dS1 S1
0.2327755087 0.2427755087 -0.0110669557 0.9889330443
0.214972605 0.224972605 0.0646582317 1.0646582317
0.3938266643 0.4038266643 -0.0790241919 0.9209758081
0.1911976504 0.2011976504 0.062570815 1.062570815
0.605898025 0.615898025 -0.268400941 0.731599059
Sheet2
90% quantile uncorrelated correlated =LZ
rho12 -0.1 eps 1 eps 2 eps 1 eps 2
mu1 and mu2 0.1 0.1 0.01 -2 0.001 -0.1990974874
var 1 and var 2 0.01 0.01 1.2 0.8 0.12 0.067598995
weight 0.33 0.67 -0.23 2.54 -0.023 0.255026809
0.45 0.17 0.045 0.0124147864 0.8 1.282
CHOLESKY 0.22 -0.14 0.022 -0.0161298241 0.85 1.44
0.1 0 0.81 0.02 0.081 -0.0061100251 0.9 1.645
-0.01 0.0994987437 0.21 0.49 0.021 0.0466543844 0.95 1.96
SIGMA -3.42 0.57 -0.342 0.0909142839 0.99 2.576
0.01 -0.001 -0.71 0.11 -0.071 0.0180448618
-0.001 0.01 0.03 -1.67 0.003 -0.166462902
r1 r2 loss sorted loss Exact loss
0.101 -0.0990974874 0.0323983249 -0.2160134045
0.22 0.167598995 -0.1850659966 -0.1937994975
0.077 0.355026809 -0.262351206 -0.1374449874
0.145 0.1124147864 -0.1232765243 -0.1338271922
0.122 0.0838701759 -0.0965801173 -0.1287073932
0.181 0.0938899749 -0.1229266499 -0.1029350879
0.121 0.1466543844 -0.1381029229 -0.0735224309
-0.242 0.1909142839 -0.0466095226 -0.018268549
0.029 0.1180448618 -0.0883632412 -0.0009512563
0.103 -0.066462902 0.009975268 0.025542858
Sheet3
path 1 path 2 path 3 path 4 path 5
t1 0.25 19.2533 34.7788 35.6238 39.5507 36.1251
t2 0.50 18.1637 25.452 24.296 34.0307 29.6701
t3 0.75 28.1132 31.2341 23.194 38.1234 31.211
strike 25
spot 25
r 0.01
alpha 0 0.01 0.02
alpha 1 0.25 0.35
alpha2 0.05 -0.05
path 1 path 2 path 3 path 4 path 5
t = 0.5 holding value 2.2007049422 7.5969076 6.5637904 0 11.9333358502
exercise value 0 0.452 0 9.0307 4.6701
t = 0.5 paysoffs 3.1054267206 6.2185342153 -1.801490639 9.0307 6.1954918932
t=0 discount average 4.538372313
t=0.25 holding value -13.7605640222 -38.613823236 -40.312328161 -48.6741217623 -41.3368462502
exercise value 0 9.7788 0 0 0
value 0 9.7543835333 0 9.0081514474 6.1800225083
4.9885114978
4.9760557952
Sheet4
dt 0.25 eps 1 eps 2
rho 12 0.3 0.46659097 0.01410045
a1 0 0.34000663 0.09450884
a2 0.05 0.2746701 0.48553626
sigma1 0.1 0.39228212 0.07740258
b1 0 0.92687015 0.47256735
b2 0.01 dW1 dW2
b3 0.2 0.47505124 0.01128036
sigma2 0.05 0.396711934 0.075607072
r0 0.01 0.565991856 0.388429008
theta0 0.05 0.438723668 0.061922064
1.21041056 0.37805388
cholesky
1 0.6
0 0.8
d theta 0 dr0 r1
0.0001544509 0.0009750512 0.0109750512
0.0003152677 0.0008967119 0.0108967119
0.0010973225 0.0010659919 0.0110659919
0.0002810552 0.0009387237 0.0109387237
0.0010713847 0.0017104106 0.0117104106
0.0111173779 ave
0.0003373411 std
0.0001508635 std err
Sheet5
corr eps 1 eps 2
1 0.6 0.46659097 0.01410045
0.6 1 0.34000663 0.09450884
Cholesky 0.2746701 0.48553626
1 0.6 0.39228212 0.07740258
0 0.8 0.92687015 0.47256735
dW1 dW2 tau1 tau2
0.47505124 0.01128036 6.4445462115 0.0141805823
0.396711934 0.075607072 5.0536047493 0.0982725637
0.565991856 0.388429008 8.3469198008 0.6146552947
0.438723668 0.061922064 5.7754192432 0.0799028075
1.21041056 0.37805388 0 0.5936272672