An accumulator option with an American-style knock-in barrier. If the underlying trades through that barrier on a fixing date, the accumulator adds to the notional a specific amount. Each time the underlying hits the barrier on a fixing date, the notional increases. On expiration date, the terminal notional becomes:

Notional + notional x (n/N)

where:

n is the number of times the underlying breaks through the barrier on the preset fixing dates.

N is the number of fixing dates over the life of the option.

The opposite of an accumulator-in option is an accumulator-out option.