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What is the probability of the price crossing a fixed barrier over the next time period t ?What does it depend on?

Excellent - thanks! This answers my question! Do you have a reference for this, i.e. how is it derived?

Is there a closed-form solution for calculating the probability that k stocks cross a barrier H, given n stocks (0 <= k <= n) with equal volatility, price at time 0 and a constant correlation between the returns of the stocks?All help would be much appreciated..

I think I was typing faster than I was thinking.. My dilemma is this:I was reading through Vasicek's legendary paper: Probabilty of Loss on Loan PortfolioIn his paper he assumes that a company defaults if the value of its assets A at time T, t>0 fall below a certain threshhold D (=the level of debt), Aka A(T)<D. Now, in my opinion a company defaults if the value of its assets drop below the threshold (=barrier) at any time during 0<t<T, aka min(0<=t<=T)A<D. This seems much more logical: If A is close to D at time 0 with, say, a reasonable amount of volatility, then Vasicek's PD will be close to 0.5, while the barrier-assumption will be close to 1.So what I was really pondering was this: If Vasicek's Loss-formula was built around a PD equation measuring the probability of crossing the D barrier before time T, as opposed to measuring the probability of ending up below the level D at T, how would this impact the pdf at the end? Ie. would it be the identical, less or more skewed as opposed to the result he gets?

My concern is mainly from an applied perspective: If I've observed a certain default rate over, say, a one year period, and I assume it to be the mean PD in the future, would the loss distribution look different, given that the underlying definition of default is also different?

What is the probability of the price crossing a different type of a barrier (not just fixed) over the next time period 0..t ?Any closed form solutions for that ? For example if the barrier is defined to be the moving average of the underlying time series...Many thanks!