n-dimensional correlated Brownian motions
Versione 1.0.3 (3,09 KB) da
Gregor Fabjan
Generate a matrix of increments from a multidimensional Brownian motion with a given vector of means and a Variance-Covariance matrix.
Functions generate a matrix of increments from a multidimensional Brownian motion with a given vector of means and a Variance-Covariance matrix.
Problem
Often 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 normally distributed as well as the fact that assuming n independent BM's whose increments are generated from a standard normal distribution (denoted
, a derived process
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
- Vector 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. Additionally, 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)
Cita come
Gregor Fabjan (2024). n-dimensional correlated Brownian motions (https://github.com/open-source-modelling/correlated_brownian_motion_matlab), GitHub. Recuperato .
Compatibilità della release di MATLAB
Creato con
R2021b
Compatibile con qualsiasi release
Compatibilità della piattaforma
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Versione | Pubblicato | Note della release | |
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1.0.3 | Link to new repository |
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1.0.2 | Project now has a website |
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1.0.1 | Link to GitHub |
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1.0.0 |
Per visualizzare o segnalare problemi su questo componente aggiuntivo di GitHub, visita GitHub Repository.
Per visualizzare o segnalare problemi su questo componente aggiuntivo di GitHub, visita GitHub Repository.