An Optimal Price Setting Rule for Market Makers

Abstract

We develop a theoretical model of the optimal rate at which a market maker adjusts price in response to the flow of buy and sell orders for an asset. A distinctive feature of our theory is our demonstration that the price rule may be expressed as a simple function of the volatilities in value and order flow. In focusing on price setting alone, we obtain a closed form solution over an infinite time horizon, that is otherwise free of most assumptions found in previous research. We show that volatilities in asset value and order flow combine non-linearly in determining the optimal pricing rule.

Keywords: Asset Pricing, Market Microstructure, Equity Pricing, Price Maker JEL Classifications: G120, D420