Optimal Bid-Ask Spread in Limit-Order Books under Regime Switching Framework

This paper advocates a regime-switching model to capture the risk of structural changes in the economy, when determining the optimal bid-ask spread in limit order books. In our model, the market-maker faces an inventory risk due to the diffusive nature of the stocks¡¯ mid-price and a transactions risk due to a Poisson arrival of market ¡°buy¡± and ¡°sell¡± orders. We propose that the intensity of the orders depend on the state of the economy, and in the event of a structural change, market makers will face different intensity of order flows, reflecting the new market conditions. In our model, the dealer is a wealth maximizing agent who dynamically manages his portfolio. We employ Hamilton-Jacobi-Bellman equation for the dynamic programming problem, and we solve the problem numerically using the Galerkin method.