I was asked this question in an interview.
There is an option as follows. It monitors the prices of two stocks A and B, and pays the difference in their prices at time $T$, if stock A has been higher than stock B all through till $T$. There is nothing paid if stock A has fallen lesser than stock B at any time before $T$.
How do we price this option?
I gave an answer by modeling the difference as a Brownian motion, and computing the probability that the zero-hitting time for the BM to be greater than $T$. However the interviewer said there was a simpler method based on option pricing.
Can anyone help me?