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Simulate and plot geometric brownian motion

• To: mathgroup at smc.vnet.net
• Subject: [mg122727] Simulate and plot geometric brownian motion
• From: Priyan Fernando <priyan.fernando at gmail.com>
• Date: Wed, 9 Nov 2011 06:22:02 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hi

Wonder if you could please help me simulate and plot geometric brownian
motion (GBM)

E.g.  dS = mew * S dt  +   sigma * S *dX

What I am trying to do is generate in Mathematica the process for a
stock/share price based on GBM

Therefore:
dS is change in share price
S is the share price  (e.g. let S start from 100)
dt is the time step (e.g. in discrete version we could have dt=1/52 so
timestep is 1 week)
mew is the drift (e.g. mew = 5%)
sigma is the volatility (e.g. sigma = 10%)
dX is brownian motion (e.g. in discrete version, dX = Sqrt(dt) * N(0,1))

What I am trying to obtain is pairs (x,y) where x is the time step and y is
the share price. And then to be able to plot this.

Thanks for your help,
Priyan.

• Follow-Ups:
  • Re: Simulate and plot geometric brownian motion
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>