Could you provide tools and/or analytic models that calculate: 1. the probability that the underlying asset will be above or below a target price at any time during a time period. 2. the probability that an asset will be outside either of two prices at any time during a time period. 3. the probability that an asset move outside both of two price targets, and of being between the target prices at some time during a given time period. Free tools are sought. If you have formulas please provide them or give links. Thanks.

Here you go: http://www.amazon.com/Complete-Guid...=sr_1_1?s=books&ie=UTF8&qid=1281270422&sr=1-1 Just about as exhaustive an answer to your questions as can be imagined and coming from Collector himself. See Ch 2.8, as well as Ch 4.17 etc. The book's bibliography section contains references to the original papers.

I thought I'd mention also that Ch 2.8 should address the question of whether it's valid to interpret delta as the probability of ending ITM at expiry.