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Jul
9
comment Why does [dz(t)]^2 converge to dt over infinitesimally short time periods?
For the first, in the original formula $T$ is not inside the summation. The sum has $N$ terms, so instead of subtracting T from the sum, you can subtract T/N from each term. For the second part - $E(\Delta z_i^2) = T/N$, so your second term is $-2 T^2/N^2,$ so the whole thing under the summation sign adds nicely.
Jul
2
comment Why does [dz(t)]^2 converge to dt over infinitesimally short time periods?
hmm, where do I miss $T/N$?
Jul
2
awarded  Editor
Jul
2
revised Why does [dz(t)]^2 converge to dt over infinitesimally short time periods?
added 801 characters in body
Jul
2
comment Why does [dz(t)]^2 converge to dt over infinitesimally short time periods?
Judging by the addendum you've made to your answer after reading mine, it's pretty clear to you, how it relates to the question. I'll expand if I have time and there is interest.
Jul
2
comment Why does [dz(t)]^2 converge to dt over infinitesimally short time periods?
no, the last asymptotic is from the law of iterated logarithm. Will try to find a good reference.
Jul
2
comment Why does [dz(t)]^2 converge to dt over infinitesimally short time periods?
@vonjd: no, "i.e. ..." part is wrong. You don't square a martingale, you square the sum before the limit, and the whole point is that 1) it converges 2) only if it's the second power. And both parts are manifestations of CLT.
Jul
2
comment Why does [dz(t)]^2 converge to dt over infinitesimally short time periods?
This explain neither convergence, nor why square is the right power. It's really CLT for a random walk.
Jul
2
answered Why does [dz(t)]^2 converge to dt over infinitesimally short time periods?
Jun
11
awarded  Tumbleweed
Jun
4
asked Do people hedge with leveraged ETFs intraday? How?
Jan
10
comment Book on market microstructure
Out of curiosity, what's so HFT oriented there?
Jan
10
answered Book on market microstructure
Dec
30
comment How to interpret beta meaningfully?
Just wanted to finish your logic to the complete answer: using the formula for beta above, one can see, that beta(A, relative to B) * beta(B, relative to A) = correlation between A and B. So one shouldn't expect them to be inverse of each over. In your example it just means, that the correlation between the returns is sqrt(0.48 * 0.74) ~ 0.59.
Oct
19
awarded  Yearling
Oct
3
awarded  Student
Oct
3
asked interest rate in cost of carry
Sep
24
comment Trader's identity in a limit book
@ CharlesM (cntd): You can look at the time gaps between consecutive trades on the feed. What you will see in the statistics, is that there will be a number of events with very small/no gaps, and the rest - with significantly larger gaps. This way you figure out for the reasonable threshold. @chrisaycock: there is no such thing, as "the same time", and I think it's extremely unlikely, that NASDAQ will receive several separate orders within 1 nanosecond.
Sep
24
comment Trader's identity in a limit book
@ CharlesM - I can't say, 0 nanoseconds or 10, but yessure about nanoseconds, but yes, that's the idea
Sep
23
answered Trader's identity in a limit book