A condition occurring in barrier options where their being knocked-in (activated) or knocked-out (deactivated) depends on a specific underlying price/ rate (e.g., interest rate reference) crossing or trading through a set barrier, technically known as an instrike or outstrike price.
Barrier discontinuity takes place if the barrier condition is satisfied only at certain times such as market close, or on specific dates. This implies that the barrier will cease to be set, and option pricing will get more complicated.
