Hi guys,I would like to find the probability that a stock will end up at time T with a price <=100. The stock has normal density and on the book which I took as a reference, after few steps the following is provided:where:I've tried to resolve the integral by myself, but the solution is quite complex. I'm not so sure that is the correct one, I guess I've missed something. Could you please tell me if the direction that I've taken to resolve this problem is correct?Also, I was wondering if there is any freeware software that could help me resolving integrals.Tanx,japanstar

shouldn't this just be N(-d2) where N() is the cumulative normal and d2 is given by

What you have is a standard normaly ditributed variable with drift mu*T and standard deviation sigma*sqrt(T).First I believe you should integrate from minus infinity to a if Y is normally distributed, secondly, the integral is not solvable analytically, there are tables for these kind of integrals.

Thanks to your hints guys, I have been able to resolve the problem. Also, I've found a web site which seems a pretty good tool to resolve ntegrals: http://integrals.wolfram.com/index.jsp