Using Historical Volatility to Estimate an Implied Move
Summary
The discussion asks whether historical volatility can be substituted for implied volatility in a formula for estimating an instrument’s move over a chosen period. It treats the calculation as a conditional estimate: if volatility stays at its historical level, that value can be used to scale a move over time, while recognizing that historical volatility describes past returns rather than a market forecast.
The responses distinguish backward-looking historical volatility from forward-looking implied volatility, which can include a volatility risk premium. They also caution that a simple symmetric price range becomes less appropriate at high volatility when volatility is defined as the standard deviation of log returns. In that setting, a log-return range maps to asymmetric price levels through exponentiation. The document offers conceptual guidance rather than a full derivation or empirical comparison, and it does not specify the exact platform conventions or annualization details needed to reproduce a particular estimate.
Key ideas
- Historical volatility can scale a projected move if volatility is assumed to persist.
- Historical volatility describes past variation, while implied volatility reflects option prices and forward-looking expectations.
- Implied volatility may differ from historical volatility because it can include a volatility risk premium.
- At high volatility, log-return ranges translate into asymmetric price levels rather than a simple symmetric price interval.
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# Converting Historical Volatility to Implied Move
# Converting Historical Volatility to Implied Move
I am trying to calculate an implied one-day move value for an instrument given its historical volatility. While I am familiar with this formula for implied volatility to implied move:
and intuition suggests this formula would hold true also for historical volatility, I am given pause by the often large difference between the two. I am obtaining historical volatility from TradingView and thinkorswim, both of which use the formula and methodologies outlined in the thinkorswim link.
I am aware that historical volatility is backwards looking, but I am simply trying to calculate the expected move over a given period of time if volatility were to remain at the historical value.
In short, I am seeking assurance in the validity of using historical instead of implied volatility in the formula pictured above. And if one wishes, perhaps an explanation of (or resource on) this often glaring difference between the two? Thank you all.
## Answer by user42108 (score 1, accepted)
https://quant.stackexchange.com/a/63112
perhaps an explanation of (or resource on) this often glaring difference between the two?
IV is forward looking and should include some risk premium. My 2c is the best reference is "Volatility Trading" by Euan Sinclair; IIRC, "Option Trading", by the same author, is an introductory version.
## Answer by XXXXXXX (score -1)
https://quant.stackexchange.com/a/79016
Since volatility exact definition is the standard deviation of log returns this above formula would actually be incorrect. Suppose that you are trying to calculate the expected 1yr move on a $100 stock with IV = 200%. Are we really going to assume that the stock will trade between (-100,300) 68% of the time?
The higher the volatility, the more this formula begins to break down. It would be correct to use the following to calculate your range at 1 year. $ P_t = 100*e^{\pm 2} $
since log returns would be $ln(\frac{P_t}{100}) = \pm 2.0$Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.