ughh!

The last week of the sem is here .. and I have a take home exam for my stochastic calculus class. Its a pretty tricky exams.. I'll say .... and infact I have been stuck on one problem for 3-4 days now. Imagine trying to solve just one problem for 3 days .. I tried looking everywhere for some hints as to how to go about solving the question, but no luck. The question is an option pricing problem. It goes something like this- There is a security that will pay you $1 after time T if a particular stock price goes below half its initial value before T.... and $0 otherwise. How much will a customer be willing to pay for this security. We have to find a fair price for this derivative. Will take up the fight again tomorrow !!