n-dimensional correlated Brownian motions

Generate a matrix of increments from a multidimensional Brownian motion with a given vector of means and a Variance-Covariance matrix.

13 Downloads

Updated 19 Sep 2022

From GitHub

View License on GitHub

Functions generate a matrix of increments from a multidimensional Brownian motion with a given vector of means and a Variance-Covariance matrix.
Problem
Offten when using for example multifactor models, the model requires correlated sources of noise. A popular choice is to use a multidimensional Brownian motion.
Solution
The proposed algorithm uses the fact that increments of a BM are normaly distributed as well as the fact that assuming n independent BM's whose increments are generated from a standard normal distribution (denoted , a derived proces has its increments distributed as where mu is the vector of desired means and L is the square root of the desired Variance-Covariance matrix (denoted E).
Inputs
  • Vecor of means for each BM `mu`
  • Variance-Covariance matrix whose diagonal elements describe the volatility of each BM and the off-diagonal elements describe the covariance `E`
  • Number of samples needed `sampleSize`
Output
  • Matrix of samples where each column represents a BM and each row a new increment
Getting started
The user is interested in generating samples from 2 Brownian motions with a correlation of 0.8. Additionaly, the first BM has a mean of 1 and a variance of 1.5. The second BM has a mean of 0 and a variance of 2. The user is interested in 480 samples.
Example of use
mu = [1; 0];
VarCovar = [1.5, 0.8; 0.8, 2];
sampleSize = 480;
CorBrownian(mu, VarCovar, sampleSize)

Cite As

Gregor Fabjan (2023). n-dimensional correlated Brownian motions (https://github.com/qnity/correlated_brownian_motion_matlab), GitHub. Retrieved .

MATLAB Release Compatibility
Created with R2021b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Versions that use the GitHub default branch cannot be downloaded

Version Published Release Notes
1.0.1

Link to GitHub

1.0.0

To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.