How to calculate probability that a stock touch a specific price within for example 3 months? (Not close at this price but touch it during whole period) Does anybody know where can I find formula to calculate this? (i would like to calculate it by my self without calculator from any page)

I doubt if there is a simple or closed-form solution for this--you would have to calculate a bunch of conditional probabilities

http://www-stat.wharton.upenn.edu/~steele/StochasticCalculus.html i think your answer is similar to chapter 1 question 1. http://www-stat.wharton.upenn.edu/~steele/Courses/955/Homework/SCFA-Ch1Ch2Solns.pdf

Look under probability to occur an eventual absorption of geometric Brownian motion and expected first hitting time. Nice free site includes excel calculator to extract these numbers under monte carlo simulation of paths. You simply enter estimated drift and variance of the instrument you are looking at. http://www.puc-rio.br/marco.ind/hittingt.html#spreadsheet

Assume Black-Scholes accurately models stock price movements. Assume you know the future volatility "sigma" of the stock's price action. Assume the stock price today is "P". Assume the price-to-be-touched is "S" (the "strike price"). The probability "X" that the stock will touch or exceed the strike price S, within T days, can be found thus: Z = ln(S/P) / (sigma * sqrt(T/365)) X = CNDF(Z) ln() = natural logarithm = log to the base e Z = Zscore = size of price move from P to S, in standard deviations CNDF() = Cumulative Normal Distribution Function Now you just construct a summation. The first term is the probability that the stock will touch or exceed the strike price within 1 day (T=1). The second term is the probability that the stock DOES NOT touch or exceed the strike price withing 1 day, times the probability that the stock touches or exceeds the strike price within 2 days. The third term is the probability that the stock DOES NOT touch or exceed within 2 days, times the probability that the stock does touch or exceed within 3 days. Create 90 terms (for 3 months), add them up, done.