I've been trying to learn options math and am getting hung up on a basic misunderstanding. From what I have gathered, to get a single day volatility from annualized volatility, you would do something like this - var dailyVol = impliedVol / sqrt(1.0 / 365); My assumption would then be that if I want to find an "x sigma" daily move to the upside or downside, I would do the following - var newPrice = exp(log(1 + dailyVol) * nSigma) * currPrice; But when reading through options trading materials, they often will state something more like this - var oneSigmaMove = currPrice * dailyVol; var newPrice = currPrice + oneSigmaMove * nSigma; This has the effect that moves to the downside represent a larger percentage change than the way that I would have interpreted "daily volatility," because it uses the same absolute price change in both the up and down directions. Additionally, a "multi-sigma" move would effectively compound with my formulation, but not in the second formulation. Which of the above calculations does "implied volatility" actually "imply?"