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The boundary conditions for Discrete Type Barrier (e.g. Up-and-Out) are: - Dirichelet boundary condition (set to 0 when spot is bigger than Barrier) on Barrier event dates - Otherwise (the other sides on barrier event dates and two sides on non-barrier dates), use Null-Gamma Neumann boundary condition

Then when we perform the backwardation, on barrier event dates, we only perform the calculation for the non-knock out areas - with the cut matrix and a vector to include the first element in the knock out areas from the V(t)

For other non-barrier dates, we should perform the backwardation using the whole matrix for all the grids (even for the date just before the barrier event date)?

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