Barrier Shifts And Overhedging

A knock-out barrier option is genuinely difficult to hedge because its risk changes discontinuously: an instant before the spot price touches the barrier the option is a normal, live position, and an instant after it can be worthless. Standard Greeks describe smooth changes in value, so they badly misprice the risk of a position whose payoff jumps to zero the moment a level is crossed. A trader who hedges only to the textbook Greeks can be caught enormously long or short gamma in the seconds around the barrier, exactly when volatility is highest.

Two practical tricks manage this. A barrier shift moves the level used for pricing and hedging purposes slightly away from the true contractual barrier — for a knock-out that the desk is short, shifting the barrier further from spot builds in a buffer, so the position starts unwinding its hedge before the real barrier is hit rather than at the moment of the actual jump. Overhedging does the same job differently: instead of moving the barrier, the desk holds a hedge sized for a slightly larger position than the option's Greeks technically call for, again buying a margin of safety against the jump.

Both techniques cost money in expectation — they hedge against a risk that may never materialize — which is why the size of the shift or overhedge is itself a risk-management decision, tuned to how much gamma risk near the barrier the desk is willing to eat.