Description Usage Arguments Value Author(s) References See Also Examples
If the process X_t is the unique strong solution of the process
dX_t = b(X_t)dt + s(X_t)dW_t,
then the Milstein Scheme is X[t+h] = X[t] + b(X[t])h + s(X[t])Z + 0.5*s'(X[t])*(Z^2 - h), where Z ~ N(0,h) (variance h), and s' is the differential function of s.
1 |
n |
integer, number of paths. |
m |
integer, number of steps, the step size will be T/m. |
x0 |
numeric, starting point of the process. |
b |
function, the drift, a function which can take a vector and returns a vector. |
s |
function, the volatility, a function which can take a vector and returns a vector. |
sx |
function, the differential of the volatility, a function which can take a vector and returns a vector. |
t0 |
double, the starting date of the process. |
T |
double, the final date of the process. |
all_dates |
logical, if TRUE, returns all steps from all paths. If FALSE, only returns the n final value X_T. |
delta |
double, the step size. |
If all_dates = TRUE
, it returns a n x m+1 matrix : n paths with m steps (+ the first value). Else, it returns a vector of length n with the simulations of the final dates X_T.
Nicolas Baradel - PGM Solutions
https://en.wikipedia.org/wiki/Milstein_method
https://pgm-solutions.com/packages
1 2 3 4 |
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 1 1.0533625 1.0271061 1.0797720 1.119593 1.1342900 1.0944747 1.1595887
[2,] 1 1.0205794 1.0217800 1.0659556 1.101957 0.9884711 1.0210811 0.9667245
[3,] 1 0.9928005 1.0306966 1.1377521 1.017713 0.9960424 0.9632566 0.9083929
[4,] 1 1.0126124 1.0367437 1.0184944 1.104423 1.1222356 1.1555864 1.2235908
[5,] 1 0.9471298 0.9294861 0.9533129 1.007129 1.0722700 1.1954079 1.2441727
[,9] [,10] [,11]
[1,] 1.0653542 0.9394955 0.9397999
[2,] 0.9240472 0.9209310 1.0066068
[3,] 0.8920531 0.9033853 1.1051406
[4,] 1.3366670 1.3319782 1.3163443
[5,] 1.2064591 1.2336388 1.3236321
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