Market Maker Profit Incentives and Phase Changes in Kyle’s Model

Summary

This paper modifies Kyle’s insider-trading framework, modeling an interaction among an informed trader, noise traders, and a market maker. The insider chooses a market-order size, after which the market maker prices the asset using the combined order flow. The market maker’s objective includes an additional revenue component tied to order flow and the bid-ask spread.

The authors derive the insider’s revenue-maximizing trade and give sufficient conditions for equilibrium, using neural-network methods to check whether the equilibrium holds. As the weight on the market maker’s revenue term changes, the model produces three pricing regimes: a linear rule without a spread, a linear mid-price with a spread, and a metastable state with zero mid-price and a large spread. These are theoretical model results; the description provides no empirical market test or details on how broadly the regimes apply.

Key ideas

• The model adds a spread- and order-flow-related revenue term to the market maker’s objective.
• The insider selects trade size before the market maker sets a price based on total order flow.
• The paper derives an insider optimum and sufficient conditions for equilibrium.
• Neural networks are used to verify the proposed equilibrium.
• Changing the market maker’s revenue incentive produces three distinct pricing regimes.

Tags

# Phase Transitions in Kyle's Model with Market Maker Profit Incentives


# Phase Transitions in Kyle's Model with Market Maker Profit Incentives









We consider a stochastic game between three types of players: an inside trader, noise traders and a market maker. In a similar fashion to Kyle's model, we assume that the insider first chooses the size of her market-order and then the market maker determines the price by observing the total order-flow resulting from the insider and the noise traders transactions. In addition to the classical framework, a revenue term is added to the market maker's performance function, which is proportional to the order flow and to the size of the bid-ask spread. We derive the maximizer for the insider's revenue function and prove sufficient conditions for an equilibrium in the game. Then, we use neural networks methods to verify that this equilibrium holds. We show that the equilibrium state in this model experience interesting phase transitions, as the weight of the revenue term in the market maker's performance function changes. Specifically, the asset price in equilibrium experience three different phases: a linear pricing rule without a spread, a pricing rule that includes a linear mid-price and a bid-ask spread, and a metastable state with a zero mid-price and a large spread.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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