How would I go about calculating a 1SD price move given that I know the stock price and implied vol. For example, AAPL is at 325 Implied Vol is 27% Answer given is 310-330 approximately I saw this example in one of Dan Sherdian's option videos and couldn't figure out how he got these numbers. Any help is appreciated.

Assumption is that std dev of distribution grows as square root of time (or variance scales linearly with time). Quotes implied vol is in annual terms. Easy back of envelope calculation: 1-day range ~= 1-yr range / sqrt(num of trading days in a year). So, 26/16 * current price = +- one day range. Typing this on iPhone, so had to be brief.

Your 1SD up/down are not equidistant, so the numbers are wrong. Do you want the maths or the QND? Use the ATM straddle premium.

Atticus, out of curiosity what is the exact math behind it? and why is it that it is asymmetrical . I've noticed it in TOS. Is it because you are using a log normal distribution ?

It's interesting how confused everyone is about the price distribution as opposed to the returns distribution(admittedly, at first glance I made this mistake too). No one has even given you a correct answer yet. Under Black-Scholes assumptions the price distribution is certainly not symmetric, it has a positive skew. The truth is that your question is not even well posed. You need to specify whether you mean standard deviation with respect to real world probabilities or risk neutral probabilities because the standard deviation of a lognormal random variable depends on the mean of the underlying normal random variable. So in fact, this question is more interesting than it seems at first glance and should be given more attention.