Market Making with Stochastic Liquidity Demand: Simultaneous Order Arrival and Price Change Forecasts

TL;DR

This paper develops an explicit model for optimal market making in a discrete-time limit order book, accounting for stochastic demand, order arrivals, and price forecasts, revealing how these factors influence spreads and inventory management.

Contribution

It introduces a novel, explicit characterization of the optimal market making strategy that incorporates stochastic demand and simultaneous order arrivals, improving upon prior models.

Findings

Demand slope randomness reduces inventory management incentives.

Positive correlation between demand slope and reservation prices widens spreads.

Simultaneous buy and sell orders decrease shadow costs and affect spread dynamics.

Abstract

We provide an explicit characterization of the optimal market making strategy in a discrete-time Limit Order Book (LOB). In our model, the number of filled orders during each period depends linearly on the distance between the fundamental price and the market maker's limit order quotes, with random slope and intercept coefficients. The high-frequency market maker (HFM) incurs an end-of-the-day liquidation cost resulting from linear price impact. The optimal placement strategy incorporates in a novel and parsimonious way forecasts about future changes in the asset's fundamental price. We show that the randomness in the demand slope reduces the inventory management motive, and that a positive correlation between demand slope and investors' reservation prices leads to wider spreads. Our analysis reveals that the simultaneous arrival of buy and sell market orders (i) reduces the shadow cost of inventory, (ii) leads the HFM to reduce price pressures to execute larger flows, and (iii) introduces patterns of nonlinearity in the intraday dynamics of bid and ask spreads. Our empirical study shows that the market making strategy outperforms those which ignores randomness in demand, simultaneous arrival of buy and sell market orders, and local drift in the fundamental price.