None really. It is still the partial derivative of the option price with respect to the underlying price. Some care needs to be taken in calculating that derivative if you are close to the barrier. Unlike the behavior at the early exercise boundary for an American option you do not have “smooth pasting” for an arbitrary barrier, so the delta is ill defined at the barrier itself.What modification for calculating Delta would there be for a barrier option?
Discretely monitored barrier options generally have unbounded deltas in a neighborhood close to the barrier and a monitoring point in time. Not a healthy product if you ask me.Weekly. I was thinking that the Delta would be 0 or go to zero (Knock in, Knock out) once the barrier is hit which would make the delta graph have a "step" in it vs a purely logarithmic path.