Most financial markets operate as double auction markets in which buyers and sellers submit limit and market orders. In this case the traders have to decide firstly whether they want to submit a buy or sell order and then secondly what the limit price of this order is. In this thesis I develop further a theoretical model based on Chatterjee and Samuelson (1983) in which two traders trade with each other in a double auction market. Assuming that both traders assign a private value to the asset they are trading, which is known only to them but not their trading partner, I determine whether the traders should submit a buy or sell order and what the optimal limit price should be. I develop a single-period model in which traders only trade once and thus cannot learn each other’s private values from trading as well as a multi-period model that allows to infer to some degree the other trader’s private value from their order submission behavior. Using this theoretical model as a benchmark, I then conducted experiments with students to evaluate whether the actual behavior of students fits the theory developed. Although we find that in general the behavior of traders is consistent with the proposed theory, there are some significant differences. Most notably traders seem to underreact to differences in their own private value, i.e. do not adjust their limit price to the extend suggested by theory. I evaluate these outcomes in light of results established results in behavioral finance.

Magíster en Ciencias de la Ingeniería, Mención Matemáticas Aplicadas / Ingeniero Civil Matemático / Se desarrolla un modelo dinámico a tiempo contínuo que permite el comercio de múltiples mercados financieros interconectados, organizados como limit order markets, en el cual agentes endógenamente toman decisiones óptimas para maximizar el valor esperado de sus ganacias. Los agentes toman sus decisiones considerando incentivos propios, condiciones de mercado, potenciales decisiones de negociación futuras y diferentes estrategias adoptadas por otros agentes. Se concentra el estudio al análisis de divulgación de profundidad y la fragmentación en el contexto de múltiples mercados. Se prueban tres escenarios principales: (i) un único mercado Transparente, (ii) un único mercado Opaco y (iii) un mercado múltiple interconectado entre una bolsa Transparente y una Opaca que comercian el mismo activo. Los resultados principales indican que, en el contexto de un único mercado, la divulgación de profundidad genera una competencia que incrementa el suministro de liquidez y, en consecuencia, reduce el spread, el ruido de mercado e incrementa la profundidad en los precios más competitivos y en el volumen total del libro. Los agentes con una valoración privada absoluta positiva del activo incrementan sus ganancias a costa de los agentes sin valoración privada, al disminuir sus costos de espera y aumentar sus ganancias por transacción. Estos beneficios son amplificados en el contexto de múltiples mercados debido a las restricciones para transar que generan una competencia más agresiva. Se encuentra que hay un flujo de liquidez hacia la componente Transparente debido a los agentes multi mercados proveedores de liquidez, lo cual reduce el spread e incrementa las profundidades. Para mantenerse atractivos, los agentes en la Bolsa Opaca también entran en competencia, lo cual reduce el spread y ruido de mercado en esta bolsa de similar manera. Los agentes multi mercados demandantes de liquidez son los que presentan el mejor rendimiento de todos, principalmente al reducir significativamente los tiempos de sus ejecuciones. / We develop a dynamic model in continuous time to simulate multi markets trading. Traders make endogenously sequential optimal decision to maximize their expected payoffs across different limit order markets, taking into account intrinsic incentives, markets conditions, potential future trading decisions and different strategies adopted by other agents. We focus our study in depth disclosure and lit fragmentation, and test three main scenarios: (i) a single Lit Market, (ii) a single Opaque Market and (iii) Multi Markets interconnected with both Lit and Opaque venues trading a single common asset. Our main results indicate that, in a single market environment, depth disclosure generates a competition that increments liquidity supply and as a consequence, reduces spread, microstructure noise and increases depth at best quotes and total depth of the book. Agents with a positive absolute private valuation of the asset increases their benefits at the expense of agents without a private valuation, by decreasing their waiting costs and increasing their money transfer. These benefits are amplified in a multi market environment due to trading restrictions that generates more aggressive competition. We find a liquidity flow to the Lit venue given by multi market liquidity suppliers, that reduces the spread and increases depths. To stay in competence agents in the Opaque Venue enter the competition as well, reducing spread and microstructure noise in that exchange too. Multi market liquidity demanders with the possibility to trade in both venues have the best performance of all agents, due to a significant reduction in their execution time.

Main goal of this thesis is improvement of an order book model so that it behaved more realistically, based on a model developed by J. Plačková in her diploma thesis in 2011. We consider this simple model for evolution of order book in which limit orders of unit size arrive according to independent Poisson processes. Frequency of buy limit orders below resp. sell limit orders above a given price level is described by demand and supply functions. Buy (resp. sell) limit orders that arrive with price above (resp. below) the current ask (resp. bid) price are converted into market orders and cancellation of orders is not allowed. We extend this model by introducing market makers who place at the same time one buy and one sell limit order with current bid and ask prices. We show how introducing market makers reduces the spread that in the original model was unrealistically large and also show a method of calculating the precise rate of market makers needed to reduce the spread to zero. 1

Cette thèse est composée de trois chapitres distincts.Dans le premier chapitre, je montre que les mesures de liquidités traditionnelles, telles que la profondeur du marché, ne sont pas toujours pertinentes pour mesurer le bien-être des investisseurs. Je construis un modèle de marché conduit par les ordres et montre qu'une offre de liquidité élevée peut correspondre à de mauvaises conditions d'éxécution pour les fournisseurs de liquidité et à un bien-être relativement faible.Dans le deuxième chapitre, je modélise la vitesse des ajustements de prix à l'arrivée de nouvelles dans les marchés conduits pas les ordres, lorsque les investisseurs ont une capacité d'attention limitée.En raison de leur attention limitée, les investisseurs suivent imparfaitement l'arrivée de nouvelles. Ainsi, les prix s'ajustent aux nouvelles après un certain délai. Ce délai diminue lorsque le niveau d'attention des investisseurs augmente.Le délai d'ajustement des prix diminue également lorsque la fréquence à laquelle les nouvelles arrivent, augmente. Le troisième chapitre présente un travail écrit en collaboration avec Thierry Foucault. Nous construisons un modèle pour expliquer en quoi le trading à haute fréquence peut générer des "mini flash crashes" (un brusque changement de prix suivi d'un retour très rapide au niveau antérieur). Notre théorie est basée sur l'idée qu'il existe une tension entre la vitesse à laquelle l'information peut être acquise et la précision de cette information. Lorsque les traders à haute fréquence mettent en oeuvre des stratégies impliquant des réactions rapides à des événements de marché, ils augmentent leur risque à réagir à du bruit et génèrent ainsi des "mini flash crashes". Néanmoins, ils augmentent l'efficience informationnelle du marché. / This dissertation is made of three distinct chapters. In the first chapter, I show that traditional liquidity measures, such as market depth, are not always relevant to measure investors' welfare. I build a limit order market model and show that a high level of liquidity supply can correspond to poor execution conditions for liquidity providers and to a relatively low welfare.In the second chapter, I model the speed of price adjustments to news arrival in limit order markets when investors have limited attention.Because of limited attention, investors imperfectly monitor news arrival. Consequently prices reflect news with delay. This delay shrinks when investors' attention capacity increases. The price adjustment delay also decreases when the frequency of new arrival increases. The third chapter presents a joint work with Thierry Foucault. We build a model to explain why high frequency trading can generate mini-flash crashes (a sudden sharp change in the price of a stock followed by a very quick rversal). Our theory is based on the idea that there is a trade-off between speed and precision in the acquisition of information. When high frequency traders implement strategies involving fast reaction to market events, they increase their risk to trade on noise and thus generate mini flash crashes. Nonetheless they increase market efficiency.

A stochastic model for the dynamics of a limit order book is evaluated and tested on empirical data. Arrival of limit, market and cancellation orders are described in terms of a Markovian queuing system with exponentially distributed occurrences. In this model, several key quantities can be analytically calculated, such as the distribution of times between price moves, price volatility and the probability of an upward price move, all conditional on the state of the order book. We show that the exponential distribution poorly fits the occurrences of order book events and further show that little resemblance exists between the analytical formulas in this model and the empirical data. The log-normal and Weibull distribution are suggested as replacements as they appear to fit the empirical data better.