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I think I understand the most common definition for historical volatility (standard deviation of log returns), but it has me puzzled because it conflicts with my intuitive idea of what volatility is. If we use standard deviation of log returns, a stock that doesn't move has 0 volatility which makes sense. But a stock that jumps up 10% daily (or drops 10% daily) everyday consistently would have constant log return which would also produce a standard deviation of 0.

This conflicts with my intuitive sense of volatility, as these stocks seem quite volatile to me. Is this definition in place specifically so that it integrates with the BS model? Why else is this one of the more standard measurements of volatility?

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    $\begingroup$ A stock that jumps 10% every single day is perfectly predictable, which personally doesn't seem volatile to me. $\endgroup$ Commented Aug 19, 2021 at 20:48
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    $\begingroup$ Agree with @rubikscube. Also, don't confuse price with return (volatility) as explained here. $\endgroup$
    – AKdemy
    Commented Aug 19, 2021 at 21:20
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    $\begingroup$ Roughly speaking volatility is "the degree of unpredictability of price changes". Or "the amplitude of the random noise moving the price around". Too simplistic perhaps, but gives you the basic idea ... . To be more precise you need a model: BM, GBM, etc. $\endgroup$
    – nbbo2
    Commented Aug 20, 2021 at 11:16

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