Re: [Quantlib-users] Simulating multiple correlated stochastic processes

Posted by xionghan on
URL: http://quantlib.414.s1.nabble.com/Simulating-multiple-correlated-stochastic-processes-tp11981p11985.html

Hi Max,
 
The Spectral method is just an eigenvalue decomposition. It is also called Principle Component Analysis.
 
Best,
Han

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Date: Thu, 26 Jun 2008 01:28:30 +0800
From: [hidden email]
To: [hidden email]; [hidden email]
Subject: Re: [Quantlib-users] Simulating multiple correlated stochastic processes

Hi,

I studied the code further. And I realized that in StochasticProcessArray class, the correlation matrix L is decomposed into a lower triangular using SalvagingAlgorithm::Spectral. Then the new triangular matrix is applied to the array of independent normal random variables.

I am not familiar with the "Spectral" analysis. However, I want to ask:
Given correlation matrix is symmetric and positive semidefinite, can I use SalvagingAlgorithm::none method (which is essentially a Cholesky decomposition) instead? And in this case, would the final results be equivelant for SalvagingAlgorithm::Spectral and SalvagingAlgorithm::none methods?

On Thu, Jun 26, 2008 at 12:08 AM, Max <max.zou@...> wrote:

Hi,

I am trying to simulate the price dynamics of 4 different assets given the correlation among them (assuming all asset returns follow geometric Brownian motion).

I have implemented the monte-carlo simulation using Quantlib classes, such as StochasticProcessArray, MultiPathGenerator, etc.

However, I am not so sure how the StochasticProcessArray implementation ensures the correlation among the 4 assets is guaranteed, given the input 4x4 correlation matrix is positive defintie. Could someone help explain this from a theoretical perspective? or point me to the related reference?

Thanks!

Best regards,
Max

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