High-Frequency Trading in a Limit Order Book

We study a stock dealer’s strategy for submitting bid and ask quotes in a limit order book. The agent faces an inventory risk due to the diffusive nature of the stock’s mid-price and a transactions risk due to a Poisson arrival of market buy and sell orders. After setting up the agent’s problem in a maximal expected utility framework, we derive the solution in a two step procedure. First, the dealer computes a personal indifference valuation for the stock, given his current inventory. Second, he calibrates his bid and ask quotes to the market’s limit order book. We compare this ”inventory-based” strategy to a ”naive” strategy that is symmetric around the mid-price, by simulating stock price paths and displaying the P&L profiles of both strategies. We find that our strategy yields P&L profiles and final inventories that have significantly less variance than the benchmark strategy.