Marco LiCalzi

Fundamentalists clashing over the book: a study of order-driven stock markets

Abstract Agent-based models of market dynamics must strike a compromise between the structural assumptions that represent the trading mechanism and the behavioural assumptions that describe the rules by which traders make their decisions. We present a structurally detailed model of an order-driven stock market and show that a minimal set of behavioural assumptions suffices to generate a leptokurtic distribution of short-term log-returns. This result supports the conjecture that the emergence of some statistical properties of financial time series is due to the microstructure of stock markets.

Tilting the supply schedule to enhance competition in uniform-price auctions

Uniform-price auctions of a divisible good in fixed supply admit underpricing equilibria, where bidders submit high inframarginal bids to prevent competition on prices. The seller can obstruct this behavior by tilting her supply schedule and making the amount of divisible good on offer change endogenously with its (uniform) price. Precommitting to an increasing supply curve is a strategic instrument to reward aggressive bidding and enhance expected revenue. A fixed supply may not be optimal even when accounting for the cost to the seller of issuing a quantity different from her target supply.

Tilting the Supply Schedule to Enhance Competition in Uniform-Price Auctions

Uniform-price auctions of a divisible good in fixed supply admit underpricing equilibria, where bidders submit high inframarginal bids to prevent competition on prices. The seller can obstruct this behavior by tilting her supply schedule and making the amount of divisible good on offer change endogenously with its (uniform) price. Precommitting to an increasing supply curve is a strategic instrument to reward aggressive bidding and enhance expected revenue. A fixed supply may not be optimal even when accounting for the cost to the seller of issuing a quantity different from her target supply.

Subextremal functions and lattice programming

Let M and N be the set of minimizers of a function f over respective subsets K and L of a lattice, with K being lower than L. This paper characterizes the class of functions f for which M is lower (resp., weakly lower, meet lower, join lower, chain lower) than N for all K lower than L. The resulting five classes of functions, called subextremal variants, have alternate characterizations by variants of the downcrossing-differences property, i.e., their first differences change sign at most once from plus to minus along complementary chains.

On a Preferential Attachment and Generalized Pólya's Urn Model

We study a general preferential attachment and Polyas urn model. At each step a new vertex is introduced, which can be connected to at most one existing vertex. If it is disconnected, it becomes a pioneer vertex. Given that it is not disconnected, it joins an existing pioneer vertex with probability proportional to a function of the degree of that vertex. This function is allowed to be vertex-dependent, and is called the reinforcement function. We prove that there can be at most three phases in this model, depending on the behavior of the reinforcement function. Consider the set whose elements are the vertices with cardinality tending a.s. to infinity. We prove that this set either is empty, or it has exactly one element, or it contains all the pioneer vertices. Moreover, we describe the phase transition in the case where the reinforcement function is the same for all vertices. Our results are general, and in particular we are not assuming monotonicity of the reinforcement function. Finally, consider the regime where exactly one vertex has a degree diverging to infinity. We give a lower bound for the probability that a given vertex ends up being the leading one, i.e. its degree diverges to infinity. Our proofs rely on a generalization of the Rubin construction given for edge-reinforced random walks, and on a Brownian motion embedding.

Zero-Intelligence Trading Without Resampling

This paper studies the consequences of removing the resampling assumption from the zero-intelligence trading model in Gode and Sunder (1993). We obtain three results. First, individual rationality is no longer sufficient to attain allocative effciency in a continuous double auction; hence, the rules of the market matter. Second, the allocative effciency of the continuous double auction is higher than for other sequential protocols both with or without resampling. Third, compared to zero intelligence, the effect of learning on allocative effciency is sharply positive without resampling and mildly negative with resampling.

The Allocative Effectiveness of Market Protocols Under Intelligent Trading

We study the performance of four market protocols that lead to allocative efficiency: batch auction, continuous double auction, specialist dealership, and a hybrid of these last two. In a former study, we compared them with respect to several additional performance criteria under the assumption of zero intelligence. This paper analyzes three performance criteria under different ways to remove the assumption of zero intelligence. The following conclusions are robust. The number of wasteful transaction is minimized by the batch auction and the dealership. Moreover, the former minimizes price dispersion and the latter minimizes time to convergence.

Learning to Make Risk Neutral Choices in a Symmetric World

Given their reference point, most people tend to be risk averse over gains and risk seeking over losses. Therefore, they exhibit a dual risk attitude which is reference dependent. This paper studies an adaptive process for choice under risk where, while maintaining reference-dependent preferences in the short run, the agent eventually learns to make risk neutral choices. The agent repeatedly faces a choice problem over monetary lotteries. At each period, she picks a lottery that maximizes the probability of meeting the current target. Right after, she plays the lottery and adjusts her reference point for the next period in the direction of the actually experienced payoff. In the long-run, the reference point settles down to a specific value and the choice behavior converges to maximization of the expected value. However, at each period the agent maintains a dual risk attitude. Therefore, learning to make risk neutral choices takes place without the agent ever learning to be risk neutral.

Symmetric Equilibria in Double Auctions with Markdown Buyers and Markup Sellers

Zhan and Friedman (2007) study double auctions where buyers and sellers are constrained to using simple markdown and markup rules. In spite of the alleged symmetry in roles and assumptions, buyers are shown to have the upper hand both in the call market and in the continuous double auction. We replicate the study and show that their formulation of the sellers’ markup strategies, while seemingly natural, is strategically unsound because of a hidden asymmetry. We introduce a symmetric set of markup strategies for the sellers and show how it explains away the paradox of buyers’ advantage in three different double-sided market protocols.

Variations on the Measure Representation Approach

Abstract The measure approach represents a preference relation over functions by the measure of their epigraphs (or hypographs). This paper proves a measure representation theorem for a class of increasing functions and shows how its proof can be modified to yield another measure representation theorem for functions of bounded variation.