# 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.

• Are you familiar with the $\mathbb{P}$ and $\mathbb{Q}$ worlds? Commented Mar 31, 2021 at 7:42
• @BobJansen Sorry, I don't believe so. Commented Mar 31, 2021 at 14:30

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.

• Thank you for the resources. Are you confirming also that you believe substituting historical vol for implied vol in the above formula is in fact accurate? Commented Apr 1, 2021 at 15:38
• @Leafthecat - what do you mean by accurate? : ) I'm not sure what you're using the formulae for. I often see them used to give an idea of the expected range over the next N-days. Commented Apr 1, 2021 at 19:46
• Exactly that, expected range over the next N days :) Commented Apr 1, 2021 at 20:33
• OK. Should be easy enough to check which provides a more accurate forecast over your horizon. Commented Apr 1, 2021 at 21:32

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 $$ln(\frac{P_t}{100}) = \pm 2.0$$