A learning market-maker in the Glosten-Milgrom model

This paper develops a model of a learning market-maker by extending the Glosten-Milgrom model of dealer markets. The market-maker tracks the changing true value of a stock in settings with informed traders (with noisy signals) and liquidity traders, and sets bid and ask prices based on its estimate of the true value. We empirically evaluate the performance of the market-maker in markets with different parameter values to demonstrate the effectiveness of the algorithm, and then use the algorithm to derive properties of price processes in simulated markets. When the true value is governed by a jump process, there is a two regime behaviour marked by significant heterogeneity of information and large spreads immediately following a price jump, which is quickly resolved by the market-maker, leading to a rapid return to homogeneity of information and small spreads. We also discuss the similarities and differences between our model and real stock market data in terms of distributional and time series properties of returns.