The Feasibility of an Index-Contingent Trading Mechanism

"Auction" or "call" trading systems are used in many stock exchanges. An essential problem in the application of these systems is that orders in one security cannot be conditioned on prices of other securities. This paper proposes and analyzes the feasibility of an index-contingent trading system. In this system, limit orders may be conditioned on an index (any weighted average of the security prices that is determined simultaneously with the prices) in addition to the asset price. Without any assumptions about traders' behavior it is shown that under a reasonable restriction on the structure of the limit orders, there is a unique solution (vector of prices) to any set of orders in all securities. Moreover, the paper presents a quick and simple algorithm that converges to the solution. This algorithm is based on an extension of the current mechanisms; therefore it can be implemented easily in any computerized auction system.