# Is this the right formula to use implied volatility to gauge probability of a stock being within a certain range? [duplicate]

I read online somewhere, and I can't find it now, that to find the probability of a stock hitting a certain price within a certain time frame, we can use Implied Volatility:

X = StockPrice * IV * SQRT(DaysTillExpire / 365)


X would then be 1 standard deviation (or a +/- 34% probability)

So first, is this accurate and second, how does this work?

• quant.stackexchange.com/questions/33019/… – amdopt Apr 21 '17 at 14:22
• Are you asking about the probability any time before expiry or at expiry only. These probabilities are all going to be risk neutral probabilities, but the one touch price will handle the case of "anytime before expiry" and the usual digital price will handle the case of "at expiry only." In the event of a flat vol smile, both the one touch and the digital are easy to price. – FinanceGuyThatCantCode Apr 21 '17 at 14:31
• It is not "within a certain time frame" but on a certain date (the expiration date). – noob2 Apr 21 '17 at 14:49