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Is there any intuition to use 1/P (inverse of the stock price) as a factor of volatility?

$VOLT = \beta_1 * \frac{1}{P} + Res$

P.S: In a research paper, I found it's related to the market micro-structure, but I don't really know in which way they are related.

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  • $\begingroup$ I might find a solution, but it seems very simple: if the prices are up we will have lower volatility ? any one can confirm that ? $\endgroup$ – mawchne Sep 23 '17 at 12:52
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This is a poor estimator of volatility. Prices suffer from lack of stationarity (making different time periods hard to compare), and aren't mean reverting like we mostly believe volatility is. For example, if an asset increases in price by a constant amount each day the volatility will seem to be going up, even though the standard deviation of the returns is 0.

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Re: high prices $\Rightarrow$ lower volatility

It's pretty common for high volatility to arise when prices are lowering. This is because prices lowering is a movement in the underlying, and thus increases vol. Volatility is generally not related to the actual price of the underlying - you would ideally like to normalize. $\frac{1}{P}$ could potentially be used for normalization.

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