High Frequency Market Making: Optimal Quoting

Abstract

We propose an inventory-based model of market making where a strategic high frequency trader exploits his speed and informational advantages to place quotes that interact with low frequency traders. We characterize the optimal market making policy analytically, illustrate that it generates endogenous order cancellations, and compute the long-run equilibrium bid-ask spread and other liquidity measures. The model predicts that the high-frequency trader provides more liquidity as he gets faster and shies away from it as volatility increases due to a higher risk of his stale quotes being picked by arbitrageurs. Competition with another liquidity provider increases improves the overall liquidity. Finally, we provide the first formal, model-based analysis of the impact of four widely discussed policies designed to regulate high frequency trading: imposing a transactions tax, setting minimum-time limits before quotes can be cancelled, taxing the cancellations of limit orders, and replacing time priority with a pro rata or random allocation. We find that these policies are largely unable to even out the speed and informational advantages of high frequency market makers.