Market Making under a Weakly Consistent Limit Order Book Model
Michigan State University
Abstract: We develop from the ground up a new market-making model tailor-made for high-frequency trading under a limit order book (LOB), based on the well-known classification of order types in market microstructure. Our flexible framework allows arbitrary volume, jump, and spread distributions as well as the use of market orders. It also honors the consistency of price move- ments upon arrivals of different order types (e.g. price never goes down on buy market order) in addition to respecting the price-time priority of LOB. In contrast to the approach of regular control on diffusion as in the classical Avellaneda and Stoikov  market-making framework, we exploit the techniques of optimal switching and impulse control on marked point processes, which have proven to be very effective in modeling the order-book features. The Hamilton- Jacobi-Bellman quasi-variational inequality (HJBQVI) associated with the control problem can be solved numerically via the finite-difference method. We illustrate our optimal trading strategy with a full numerical analysis, calibrated to the order-book statistics of a popular ETF. Our simulation shows that the profit of market-making can be seriously overstated under LOBs with inconsistent price movements.