"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.

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.

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.

Using NASDAQ high frequency trading (HFT) and minute-by-minute Limit Order Book (LOB) data over 120 sample stocks in 10 weeks between 2008-2010, including the week of the Lehman Brothers crisis, we study how trading activities of HFTs, NHFTs (Non-HFTs) and their order placements interact, and affect overall market quality. We capture order placements via the depth (step) and the height (price) dimensions along the LOB. We first document that HFTs are active not only at the top of the LOB, but their orders are placed along the LOB with an average around the 5th step, slightly ahead of NHFTs who on average are close to the 6th step. Generally, both HFTs and NHFTs are more aggressive in order placement with large stocks and hidden orders and HFT orders are further ahead during the crisis week, though price-wise they all back off somewhat with more conservative placements by NHFTs. In market turmoil, whenever HFTs see NHFTs trade among themselves, they become less aggressive in order placement. However, when HFTs trade, other HFT orders become more aggressive by moving ahead. On the contrary, NHFTs generally become more aggressive when other NHFTs supply liquidity in trading, and more conservative when HFTs are the supplier. We find mixed results on the impact of HFTs order placements and trading activities on market quality by different measures, but aggressive orders by HFTs and NHFTs both are related with decreases in short-term market volatility. Our findings highlight the importance of not only studying HFTs and NHFTs activities along the LOB, but also in both depth and height dimensions, instead of only at the market inside quotes.

Moderne statistische und ökonometrische Methoden behandeln erfolgreich stilisierte Fakten auf den Finanzmärkten. Die vorgestellten Techniken erstreben die Dynamik von Finanzmarktdaten genauer als traditionelle Ansätze zu verstehen. Wirtschaftliche und finanzielle Vorteile sind erzielbar. Die Ergebnisse werden hier in praktischen Beispielen ausgewertet, die sich vor allem auf die Prognose von Finanzmarktdaten fokussieren. Unsere Anwendungen umfassen: (i) die Modellierung und die Vorhersage des Liquiditätsangebotes, (ii) die Lokalisierung des ’Multiplicative Error Model’ und (iii) die Erbringung von Evidenz für den empirischen Zustandsfaktorparadox über Landern. / Modern methods in statistics and econometrics successfully deal with stylized facts observed on financial markets. The presented techniques aim to understand the dynamics of financial market data more accurate than traditional approaches. Economic and financial benefits are achievable. The results are here evaluated in practical examples that mainly focus on forecasting of financial data. Our applications include: (i) modelling and forecasting of liquidity supply, (ii) localizing multiplicative error models and (iii) providing evidence for the empirical pricing kernel paradox across countries.

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.

The intention of this thesis is to provide a primitive mathematical model for a financial market in which tradings affect the asset prices. Currently, the idea of a price-volume relationship is typically used in the form of empirical models for specific cases. Among the theoretical models that have been used in stock markets, few included the volume parameter. The thesis provides a general theoretical model with the volume parameter for the intention of a broader use. The core of the model is the correlation between trading volume and stock price, indicating that volume should be a function of the stock price and time. This function between price and time was made visible by the use of the trading volume process, also known as the Limit Order book. The development of this model may be of some use to investors, who could build their wealth process based on the dynamics of the process found through a Limit Order Book. This wealth process can help them build an optimal trading strategy design.

High Frequency Trading (HFT) algorithms are automated feedback systems interacting with markets to maximize returns on investments. These systems have the potential to read different resolutions of market information at any given time, where Level I information is the minimal information about an equity--essentially its price--and Level II information is the full order book at that time for that equity. This paper presents a study of using Recurrent Neural Network (RNN) models to predict the spread of the DOW Industrial 30 index traded on NASDAQ, using Level I and Level II data as inputs. The results show that Level II data does not significantly improve the prediction of spread when predicting less than 100 millisecond into the future, while it is increasingly informative for spread predictions further into the future. This suggests that HFT algorithms should not attempt to make use of Level II information, and instead reallocate that computation power for improved trading performance, while slower trading algorithms may very well benefit from processing the complete order book.

We study optimal order placement in a limit order book. By modelling the limit order book dynamics as a Markov chain, we can frame the purchase of a single share as a Markov Decision Process. Within the framework of the model, we can estimate optimal decision policies numerically. The trade rate is varied using a running cost control variable. The optimal policy is found to result in a lower cost of trading as a function of the trade rate compared to a market order only strategy. / Vi studerar optimal orderläggning i en limit orderbok. Genom att modellera dynamiken av inkommande ordrar som en Markov kedja så kan vi formula optimal orderläggning som en Markov Decision Process. Inom ramverket av modellen så kan vi skatta optimala strategier numeriskt. En löpande kostnad används som en kontrollvariabel för handelstakten av den optimala strategin. Vi finner att den optimala strategin resulterar i en lägre handelskostnad som funktion av deltagande jämfört med en marknadsorder strategi.