In one aspect, the invention comprises a system for enabling a crossing system operator to calculate a rebate payment to a second participant for executing the block order of a first participant based on at least one of: (a) a difference between a benchmark price and an execution price of the block order; (b) total volume of block execution; and (c) an amount that decays exponentially with the time between the first participant's order and the order's execution by a liquidity provider.