I'm looking for a math formula that can give me the probability that a stock price will reach (or move beyond) a certain target price within a certain time frame. I'm imagining this formula would be something a "one touch" exotic option calculator would use. Where is takes into consideration things like: Current stock price Target strike price Volatility Risk Free interest Time duration etc. Can anybody help me with this? (I would also be interested in free or low cost calculators that can do this, but I think in the end I also want the actual formula).