A Combinatorial Auction with Equilibrium Price Selection

Abstract: Financial markets use auctions to provide accurate liquidity snapshots for traded instruments. Combination orders, such as time spreads require the atomic trading of more than one security contract. In order to auction such complex order types, a new design, which considers all contingent instruments simultaneously, is required. This work develops an optimization model and a software implementation of the dualsided multi-unit combinatorial auction problem. The optimization objective is finding an equilibrium price vector and a winner selection such that the auction turnover is maximized. The auction requirements are modeled as a discrete optimization problem, suitable for standard integer programming solvers. The model’s correctness and tractability are tested using synthetically generated orders as well as real market data. Test results with both synthetic and authentic orders produced equilibrium prices within 3% of the expected instrument valuations, using closing prices as a benchmark, indicating high accuracy of the solutions. The use of combinatorial auctions exposes greater liquidity and overall turnover, both valuable to exchanges that receive large numbers of combination orders.