1. A computer-based system for opening trading in options, comprising: a plurality of input devices to receive from each one of a plurality of market makers a current position, a desired target position and market maker orders for options series; an order entry system for receiving public orders for options series; and a controller, coupled to the plurality of input devices and the order entry system, the controller comprising (a) means for determining a set of prices for each options series that will maximize a weighted volume of trades across all option series at the opening, (b) means for executing all orders that can occur at the set of prices, (c) means for determining a residual imbalance of non-executed public orders, and p2 (d) means, utilizing the current position and the desired target position of each one of the plurality of market makers, for assigning the residual imbalance of non-executed public orders to individual ones of the plurality of market makers so as to minimize a cumulative measure of deviation between the desired target position and the current position of each market maker.