Instantaneous Order Impact and High-Frequency Strategy Optimization in Limit Order Books

Abstract

We propose a limit order book (LOB) model with dynamics that account for both the impact of the most recent order and volume imbalance. To model these effects jointly we introduce a discrete Markov chain model. We then find the policy for optimal order choice and control. The optimal policy derived uses limit orders, cancellations and market orders. It looks to avoid non-execution and adverse selection risk simultaneously. Using ultra high-frequency data from the NASDAQ stock exchange we compare our policy with other submission strategies that use a subset of all available order types and show that ours significantly outperforms.