# Monte Carlo simulation using geometric Brownian motion

I'm relatively new to Mathematica programming, so forgive my rather unsophisticated question: I'm trying to do a Monte Carlo simulation using geometric Brownian motion (GBM). I want to write a indicator function which produces is 1 if my GBM stays within a certain corridor [L, U]. I found a function which produces the paths of my GBM:

data = RandomFunction[
GeometricBrownianMotionProcess[0.01, .15, 100], {0, 1, .01}, 100]


How can I access data so that I can write the indicator function?

EDIT: Ive got a follow up question: Let's say one sample path is the following list

pts=data["Paths"]
pts
{{0,100},{0.01,98}...}


How can I select from all my pahts only those values where the x-variable is >=1? I tried Select[pts,#1.0&], but this gives me an empty list.

• Try data["Paths"]. It's explained in the docs. Commented Jan 28, 2013 at 17:25

You can get the state values for every with data["States"], which you can then easily feed into a indicator function.

data = RandomFunction[
GeometricBrownianMotionProcess[0.01, .15, 100], {0, 1, .01}, 100];
corridorIndicator[data_, upperBound_, lowerBound_] :=
Boole[Max@# < upperBound && Min@# > lowerBound] & /@ data
corridorIndicator[data["States"], 120, 80]

(*{1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1,
1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,
1}*)


EDIT: You just need to make sure you get the syntax for Select correct.

data2 = RandomFunction[
GeometricBrownianMotionProcess[0.01, .15, 100], {0, 1.3, .01}];
Select[#, #[[1]] >= 1 &] & /@ data2["Paths"]

(*{{1., 136.038}, {1.01, 133.344}, {1.02, 136.278}, {1.03,
134.923}, {1.04, 131.44}, {1.05, 131.136}, {1.06, 130.272},
{1.07, 132.126}, {1.08, 130.555}, {1.09, 126.961}, {1.1,
129.282}, {1.11, 128.943}, {1.12, 129.941}, {1.13, 128.51},
{1.14, 126.807}, {1.15, 127.05}, {1.16, 129.184}, {1.17,
129.768}, {1.18, 130.598}, {1.19, 129.944}, {1.2, 128.456},
{1.21, 129.06}, {1.22, 128.27}, {1.23, 129.513}, {1.24,
128.668}, {1.25, 128.651}, {1.26, 127.765}, {1.27, 128.401},
{1.28, 127.564}, {1.29, 126.732}, {1.3, 127.631}}*)

• (In more recent versions, "States" has been renamed to "ValueList" in the official documentation, although as of v.13 the undocumented "States" still continues to work just fine. Commented Dec 15, 2021 at 15:10