A traded warrant (and a type of barrier warrants) in which the barrier slowly approaches an in-the-money status (in-the-money side of the strike price) over its life. It is fitted with a slowly adjustable barrier that would allow the holder to tap to long term gains while the value of the warrant at expiration being path-dependent. As in a typically barrier warrant, the value of the warrant will be determined, at expiration, based on the path followed by the underlying price over the warrant’s life.