# Tag Info

8

Yes, you need Cholesky factorization. You can find the general idea here: http://www.goddardconsulting.ca/option-pricing-monte-carlo-basket.html Plus the implementation in MATLAB here: http://www.goddardconsulting.ca/matlab-monte-carlo-assetpaths-corr.html The code in general should be easily translatable. The only difficulty is the Cholesky factorization ...

3

How about an O(N log(n)) solution ? To be a viable trading strategy, you often expect them variances to be similar, so just calculate ordinary volatility and put it in an ordered array. Of course that's going to be period dependent, so pick a few arbitrary periods and see which instruments end up being together. Then you get clusters of vastly smaller ...

2

I think that your problem can be solves by using another estimator for your covariance matrix. A so called shrinkage estimator leads to covariance matrix that is non-singular. Then a Cholesky decomposition should work (maybe there is even a short-cut in the shrinkage world, I will check alter on). The R package corpcor contains functions to perform ...

1

You can use the either, as both necessarily are symmetric positive definite; covariance is a personal preference. It's really just a matter of scaling, as $\mathcal{N}(0,\Sigma)$ is distributionally $\sqrt{\Sigma} \mathcal{N}(0,1)$. Correlation would require additional scaling (i.e. multiplication of every $\mathcal{N}(0,\rho)$ element by its respective ...

1

Let $t$ be the number of days (time periods), and let $p$ be the number of assets. You have $t=1000$ and $p=10000$. For any given dataset, it is assumed that the sample covariance matrix $\mathbf{C}$ accurately represents the population covariance matrix $\boldsymbol{\Sigma}$, however, as $p \rightarrow t$ or if $p > t$ (as in your case), the ...

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