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I'm generating with Monte Carlo simulation some stock price $X$.
Once I have the stock price sample, I want to cluster it with 100 points $\hat{X}$.

My problem is that the error associate with my k-mean clustering $$ E \lVert X - \hat{X} \rVert^2, \tag{1} $$ doesn't decrease with the number of simulation $n$.
My cluster $\hat{X}$ is obtained with Lloyd algorithm and SciKit learn.

I looked at the empirical pdf of X, obtained through Monte Carlo, and it seems to be very heavy tail.
Is this the reason why my k-mean error grows with $n$?
Do I need $n$ to be really really large?

How can I quantize $X$ so that the error (1) is small?

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