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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.

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

1 Answer 1

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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}}*)
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  • $\begingroup$ (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. $\endgroup$ Commented Dec 15, 2021 at 15:10

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