Wanted to ask a question on formulation specifically on knock-out options:AS long as the underlying is above K_t during the life of the option its a standard Euro call at maturity.So the SDE is the BS SDE as long as S > KAnd say if the option is knocked out the payoff is G if S <= KSo heuristically approaching is the pricing formula:Value of Knock-Out = e^-r(T-t)* [ [BS Call(S,K) Price ] * N(d2) + G * (1 - N(d2)) ]where N(d2) is prob [ S > K]Is this correct ? --- If not what would be the correct approach to solving the SDE when the expiration date is random?Any help much appreciatedZakduka

I think you're on the right track.Let's say take a european up-and-out call strike X, barrier H (H>X). Closed form models use the REFLECTION PRINCIPLE.ie. take your normal Log-Normal PDF for S at maturity. Now consider all the stocks trhat have ended over the barrier H. For each stock path that hits H and carries on to be above H at maturity there also exists its reflection that hits H (or was very very close) and ends up below H at maturity.Therefore the PDF must be augmented by subtracting the area to the right of H from the left of it. This causes the PDF to be zero at H