Turn on suggestions

Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type.

Showing results for

Options

- RSS Feed
- Mark Topic as New
- Mark Topic as Read
- Float this Topic for Current User
- Bookmark
- Subscribe
- Mute
- Printer Friendly Page

🔒 This topic is **solved** and **locked**.
Need further help from the community? Please
sign in and ask a **new** question.

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Posted 06-11-2015 09:36 AM
(2814 views)

Is there a way to simulate data points that have been drawn from a Geometric Brownian Motion (Weiner Process)?

I am looking at this function:SAS(R) 9.2 Language Reference: Dictionary, Fourth Edition

But I don't see an option for a Weiner process.

I know the Black Scholes internally simulates a Weiner process but is it possible to see what a set of 10,000 numbers drawn from a Weiner process looks like?

1 ACCEPTED SOLUTION

Accepted Solutions

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

I'll show you the standard Weiner process (mean=0, std dev=1) and you can generalize it if necessary.

A reference is https://me.ucsb.edu/~moehlis/APC591/tutorials/tutorial7/node2.html

The key observation is that the STEP SIZES of the Weiner process are Gaussian distribution, so you can use the RAND function in the DATA step to simulate the step sizes. In SAS/IML, you can use the RANDGEN or RANDFUN functions to generate the normally distributed step sizes.

proc iml;

/* simulate N time steps from Weiner process on interval [0,Tf] */

N = 1000;

Tf = 5;

call randseed(12345);

/* algorithm: step sizes are normally distributed */

N = N-1; /* X(0)=0, so N-1 random values */

dt = Tf/N;

sd = sqrt(dt);

steps = randfun(N, "Normal", 0, sd); /* random step sizes */

x = 0 // cusum(steps); /* X(0)=0 */

5 REPLIES 5

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

I suggest you post this under the "SAS Statistical Procedures" and "SAS/IML Software and Matrix Computations" forums, I think you'll be more likely to catch the eye of someone familiar with this topic.

Tom

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Thanks Tom! **eagles_dare13**, I moved this thread to the SAS/IML community.

Anna

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

I'll show you the standard Weiner process (mean=0, std dev=1) and you can generalize it if necessary.

A reference is https://me.ucsb.edu/~moehlis/APC591/tutorials/tutorial7/node2.html

The key observation is that the STEP SIZES of the Weiner process are Gaussian distribution, so you can use the RAND function in the DATA step to simulate the step sizes. In SAS/IML, you can use the RANDGEN or RANDFUN functions to generate the normally distributed step sizes.

proc iml;

/* simulate N time steps from Weiner process on interval [0,Tf] */

N = 1000;

Tf = 5;

call randseed(12345);

/* algorithm: step sizes are normally distributed */

N = N-1; /* X(0)=0, so N-1 random values */

dt = Tf/N;

sd = sqrt(dt);

steps = randfun(N, "Normal", 0, sd); /* random step sizes */

x = 0 // cusum(steps); /* X(0)=0 */

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Thank you. I copied your code but am getting:

ERROR: Invocation of unresolved module RANDFUN

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Then replace that line with

steps = j(N,1);

call randgen(steps, "Normal", 0, sd); /* random step sizes */

**Available on demand!**

Missed SAS Innovate Las Vegas? Watch all the action for free! View the keynotes, general sessions and 22 breakouts on demand.

Multiple Linear Regression in SAS

Learn how to run multiple linear regression models with and without interactions, presented by SAS user Alex Chaplin.

Find more tutorials on the SAS Users YouTube channel.