"On a stock exchange, trading activity has an impact on stock prices. Market agents place limit orders, which come in the form of bids and asks. These orders wait in the market to be executed when another agent agrees to fulfill the transaction. We examine an "inventory-based" quoting strategy model developed by Marco Avellaneda and Sasha Stoikov. We expand on their work by developing a method to calibrate the model to market data using limit order data provided by Morgan Stanley. We consider solving a least squares problem which fits the model to the data using a sensitivity parameter."

We analyse the steady-state behaviour of two different models with collaborating queues: that is, models in which 'customers' can be served by many types of 'servers', and 'servers' can process many types of 'customers'. The first example is a large-scale service system, such as a call centre. Collaboration is the result of cross-trained staff attending to several different types of incoming calls. We first examine a load-balancing policy, which aims to keep servers in different pools equally busy. Although the policy behaves order-optimally over fixed time horizons, we show that the steady-state distribution may fail to be tight on the diffusion scale. That is, in a family of ever-larger networks whose arrival rates grow as O(r) (where r is a scaling parameter growing to infinity), the sequence of steady-state deviations from equilibrium scaled down by sqrt(r) is not tight. We then propose a different policy, for which we show that the sequence of invariant distributions is tight on the r (1/2+epsilon) scale, for any epsilon > 0. For this policy we conjecture that tightness holds on the diffusion scale as well. The second example models a limit order book, a pricing mechanism for a single-commodity market in which buyers (respectively sellers) are prepared to wait for the price to drop (respectively rise). We analyse the behaviour of a simplified model, in which the arrival events are independent of each other and the state of the limit order book. The system can be represented by a queueing model, with 'customers' and 'servers' corresponding to bids and asks; the roles of customers and servers are symmetric. We show that, with probability 1, the price interval breaks up into three regions. At small (respectively large) prices, only finitely many bid (respectively ask) orders ever get fulfilled, while in the middle region all orders eventually clear. We derive equations which define the boundaries between these regions, and solve them explicitly in the case of iid uniform arrivals to obtain numeric values of the thresholds. We derive a heuristic for the distribution of the highest bid (respectively lowest ask), and present simulation data confirming it.

This paper provides microstructure models of order-driven market to analyze the dynamic dependencies of order strategy, price formation and order book information. This study gradually derives three models to shed light on those dynamic dependencies: risk-neutral order-submission model, risk-averse order-submission model and revision order-submission model based on order book information. Those inferences support that the order-driven market dynamically adjusts the bid/ask at any moment to generate enough price improvement return in order to cover the fluctuations of the adverse selection risk and the non-execution risk faced by limit order submitters of both side. In risk-neutral order-submission model, the model anatomizes adverse selection cost and bid-ask spread under risk-neutral preference of order submitters. This study finds that adverse selection cost comprises three components: arrival probability of informed traders, execution probability of setting price of limit order, cost-to-benefit ratio of investment. In risk-averse order-submission model, the model analyzes the optimal order-submission behavior of risk-averse uninformed traders. This study finds that the asset volatility is the key determinant of the adverse selection risk and the non-execution risk, and thereby the bid-ask spread is associated with the asset volatility. The novelty approach of this model could connect both previous risk-neutral models of Handa, Schwartz and Tiwari (2003) and Foucault (1999), which are the special cases of the reduced form of this model. In revision order-submission model, the model analyzes adverse selection costs and price formation of bid-ask spread, dynamically adjusted by previous state of limit order book in an electronic limit order market. Using order book data from the Taiwan Stock Exchange, the empirical analysis corroborates the following findings: (1) the state of the limit order book significantly affects subsequent order aggressiveness; (2) adverse selection cost and spread are negatively associated with the precision of order book information; (3) information effects of limit order book on the bid-ask spread provide strong support for the model.

Autor no autoriza el acceso a texto completo de su documento hasta el 15/1/2021. / Ingeniero Civil Industrial / Se presenta un modelo dinámico de múltiples mercados financieros, 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 trading futuras y diferentes estrategias adoptadas por otros agentes. Para efectos de la presente investigación, se compara el escenario de un único mercado financiero ( single market ) con un escenario de dos mercados interconectados que compiten por el flujo de órdenes ( multi markets ). Los resultados indican que la posibilidad de transar en múltiples mercados, beneficia ampliamente a agentes sin valoración privada por el activo, ya que buscan oportunidades de transar en ambos mercados, mientras que perjudica el bienestar de agentes con motivación intrínseca para transar, dado que obtienen peores condiciones de negociación. Por otro lado, se observa una reducción en varias medidas de liquidez en multi markets, lo que sugiere la existencia de externalidades positivas asociadas a mercados consolidados.

Title: Volatility bursts and order book dynamics Author: Jana Plačková Department: Department of Probability and Mathematical Statistics Supervisor: Dr. Jan M. Swart Supervisor's e-mail address: swart@utia.cas.cz Abstract: The presented paper studies the dynamics of supply and demand through the electronic order book. We describe and define the basic rules of the order book and its dynamics. We also define limit and market orders and describe the differences between them and how they influenced the evolution of ask, bid price and spread. Next part of the paper is dedicated to the de- scription and definition of volatility and its basic models. The brief overview about volatility clustering and its modeling by economists and physicists can be found in the following part. In the last part we introduce a simple model of order book in which we observe ask, bid price and spread. Then we study the empirical distribution of spread and try to find its probability distribu- tion. The volatility clustering is then observed through the relative returns of spread. In the last part we introduce some possible improvement of the model. Keywords: volatility clustering, order book, limit orders, market orders 1

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.

Doctor of Philosophy / This dissertation presents the results of three empirical studies on price formation and liquidity in financial futures markets. The research entails three related areas: the effect of taxes on the prices of Australian stock index futures; the efficiency of the information transmission mechanism between the cash and futures markets; and the price and liquidity impact of large trades in interest rate and equity index futures markets. An overview of previous research identifies some important gaps in the existing literature that this dissertation aims to resolve for the benefit of arbitrageurs, investment managers, brokers and regulators.

According to the empirical findings from evolution of liquidity, this dissertation constructs an optimal order submission strategy model within which a mixture of market and limit orders can be submitted by both informed and uninformed traders. In the Stacklberg Game Model, informed traders with short-lived private information are regarded as leaders, and uniformed traders with learning behaviors are referred as followers. Our theoretical findings conclude as follows: Firstly, the order strategies of all traders can be characterized as coming under one of seven regimes, pure market buy orders, a combination of market and limit buy orders, pure limit buy orders, a combination of limit buy and limit sell orders, pure limit sell orders, a combination of market and limit sell orders, and pure market sell orders. Traders will select their optimal trading strategy according to the regime within which their liquidation value falls. Parlour (1998) is a special case of this study. Secondly, an increase (reduction) in liquidation value will result in a non-linear increase in the optimal proportion of market order submissions by buyers (sellers). Thirdly, the probability of submitting limit orders for uniformed traders increases when information traders get large profit from the private information. The extreme case is uniformed traders only submit limit orders. This result is consistent with Foucault (1999). Fourthly, the price interval will be much wider when limit orders are submitted by uniformed traders than by informed traders. The reasons are that uniformed traders have no private information and that they are high risk aversion. Finally, numerical illustrations confirm the reliability of this model.

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Doctor of Philosophy / This dissertation presents the results of three empirical studies on price formation and liquidity in financial futures markets. The research entails three related areas: the effect of taxes on the prices of Australian stock index futures; the efficiency of the information transmission mechanism between the cash and futures markets; and the price and liquidity impact of large trades in interest rate and equity index futures markets. An overview of previous research identifies some important gaps in the existing literature that this dissertation aims to resolve for the benefit of arbitrageurs, investment managers, brokers and regulators.