Let’s say a stock trades at $45 today and has IV of 92%. I wanna get a rough range of where the stock might be in a week from now, let’s say $32 to $58 in a week, based on the IV 92%. How do I get that? And if I estimate price to be $x, is there a probability associated with that happening? Thank you.
As an estimate, the annualized IV of 92% translates to a weekly standard deviation of 92% * sqrt(7/365) = 13%. Assuming a lognormal distribution, this means the stock price has a 68% chance of being between $45 * exp(-0.13) = $39.50 and $45 * exp(0.13) = $51.20 in a week. Likewise, it has a 95% chance of being between about $35 and $58.
You can also estimate these probabilities from the prices of individual options (if there exist options expiring in a week): The delta of a call option is approximately the probability that it will expire in the money.