New answers tagged brownian-motion
2
You want to work directly with $\overline{X}$, and not some other r.v. with the same distribution, since equivalence in distribution doesn't imply that correlation remains the same. For ease of notation, I'll assume that $\mu = 0$ and $\sigma = 1$. I claim that
$$
\text{cov}\left(\overline{X},X \right) = \frac{1}{t} \int_0^t s \ ds.
$$
Note that this is ...
7
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 ...
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