# Modeling geometric Brownian motion with an Ito process [closed]

I am trying to model geometric Brownian motion using ItoProcess. I am not sure why I am getting negative values in the output.

I am not using GeometricBrownianMotionProcess because I want to model other SDE also.

I am not able to figure out the problem with my code.

r = 33;
s = 8;
sde =
ItoProcess[
\[DifferentialD]z[t] ==
r z[t] \[DifferentialD]t + s z[t] \[DifferentialD]w[t],
z[t], {z, 0.01}, t, w \[Distributed] WienerProcess[]];

sol = RandomFunction[sde, {0, 10, 0.01}];

ListLinePlot[sol, Filling -> Axis]


• PDF[sde[t]] and similar look fine. It's possibly a numerical issue due to the huge rate of return you are using, 3300%. – b.gates.you.know.what Sep 12 '20 at 9:17
• ^ also the s is really high. Try r = .33; s = 0.1; instead and it looks more reasonable. – flinty Sep 12 '20 at 11:44
• ^^ thanks! For reasonable values of r and s it is working fine. – S_R Sep 12 '20 at 12:55