The share of market making conducted by high-frequency trading (HFT) firms has been rising steadily. A distinguishing feature of HFTs is that they trade intraday, ending the day flat. To shed light on the economics of HFTs, and in a departure from existing market making theories, we model a profit maximizer HFT that has access to unlimited leverage intraday but must fund any end-of-day inventory at an exogenously determined cost. We provide a complete solution to the discrete-time control problem using the invariant concave structure of the value function. We find that smooth fit holds on the boundaries, and hence the value function is continuously differentiable in the inventory level at any time.
Even though the inventory costs only occur at the end of the day, they impact intraday price and liquidity dynamics. This gives rise to an intraday endogenous price impact mechanism. As time approaches the end of the trading day, the sensitivity of prices to inventory levels intensifies, making price impact stronger and widening bid-ask spreads. Moreover, imbalance of buy and sell orders may catalyze hikes and drops of prices, even under fixed supply and demand functions. Empirically, we show that these predictions are borne out in the U.S. Treasury market, where bid-ask spreads and price impact tend to rise towards the end of the day. Furthermore, price movements are negatively correlated with changes in inventory levels as measured by the cumulative net trading volume.

(joint work with Tobias Adrian, Erik Vogt, and Hongzhong Zhang) Speaker(s): Agostino Capponi (Columbia University)