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I am currently reading the book Options, Futures and Other Derivatives from John C. Hull. In the Chapter of Introducing the Balck-Scholes Model, it says:

The standard error of this estimate can be shown to be approximately $\hat{\sigma}/\sqrt{2n}$, where $\hat{\sigma}$ is the estimated sample standard deviation, $n$ is the number of samples.

Does anyone have any idea why is $\sqrt{2n}$ and not $\sqrt{n}$?

P.S.

I have sent a Email to Prof. John C. Hull, he says: "It is tied in with the properties of the Chi squared distribution", anyone has a clue?

Stephen Ge
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    I guess $\hat \sigma$ is the estimated population SD, based on a sample. And that $n$ is the number of observations. Without knowing the model, I can't say why the "2" is there. Wikipedia on 'Black-Scholes' didn't help me. Can you elaborate a bit? What estimator has this SE? – BruceET Aug 31 '16 at 17:00
  • For anyone who needs more information to answer the question, you can find the relevant text on page 305 here: http://polymer.bu.edu/hes/rp-hull12.pdf – smcc Aug 31 '16 at 18:05
  • It seems to come from the $\frac12$ in Itô's lemma – Henry Aug 31 '16 at 19:25
  • I have sent a Email to Prof. John C. Hull, he says: "It is tied in with the properties of the Chi squared distribution", anyone has a clue? – Stephen Ge Aug 31 '16 at 20:49

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