The equity trading of today is fragmented across regulated markets (RMs) and multilateral trading facilities (MTFs). Despite being legally very similar Busch (2017), market participants have reported that they attract different types of traders. Market dynamics arise from the interactions between all market participants (agents) Kyle (1985). Price impact is an important part of these dynamics which, for the most part, can be explained by the competition between liquidity takers and liquidity providers Bouchaud et al. (2009). Hence, this thesis studies whether price impact is venue dependent by using the transient impact model, developed by Bouchaud et al. (2004), on Nordic stocks listed at Nasdaq but also traded on London based MTFs. Furthermore, MiFID II and entailing legislation introduced a considerable amount of changes to the financial markets, the effects of which on price impact will also be subject to investigation here. The findings indicate that price impact is indeed venue dependent, where RMs show less price impact than the MTFs. The effects of MiFID II are vague but seems to have lowered the temporal aspect of price impact for the MTFs, while the effects on the RMs are less evident. / Dagens aktiehandel är fragmenterad över reglerade marknader och multilaterala handelsplattformar (MTF-plattformar), trots att de är juridiskt väldigt lika Busch (2017), så har marknadsaktörerna rapporterat att de attraherar olika typer av aktörer. Marknadens dynamik uppstår ur interaktionen mellan dess aktörer Kyle (1985). Prispåverkan är en viktig del av denna dynamik som, för det mesta, kan förklaras av konkurrensen mellan likviditetstagare och likviditetsgivare (Bouchaud et al. 2009). Således undersöker denna uppsats om prispåverkan skiljer sig mellan handelsplatser genom att använda en transient prispåverkansmodell, utvecklad av Bouchaud et al. (2004), på handelsdatat från nordiska aktier listade på Nasdaq, men som även handlas på MTF-platformar i London. Introduktionen av MiFID II och tillhörande lagstiftning har inneburit betydande förändringar för den finansiella marknaden, vilkas effekter på prispåverkan vid aktiehandel också kommer att undersökas här. Fynden i denna studie indikerar att prispåverkan är handelsplatsberoende, där priset påverkas mindre på reglerade marknader än på MTF-plattformar. Effekterna av MiFID II är vaga men verkar ha sänkt den temporala aspekten av prispåverkan och då främst för MTF-plattformarna, medan effekterna på de reglerade marknaderna är mindre framträdande.

Financial markets perform two major functions. The first is the provision of liquidity in order to facilitate direct investment, hedging and diversification; the second is to ensure the efficient price discovery required in order to direct resources to where they can be best utilised within an economy. How well financial markets perform these functions is critical to the financial welfare of every individual in modern economies. As an example, retirement savings across the world are mostly invested in capital markets. Hence, the functioning of financial markets is linked to the standard of living of individuals. Technological advancements and new market regulations have in recent times significantly impacted how financial markets function, with no period in history having witnessed a more rapid pace of change than the last decade. Financial markets have become very complex, with most of the order execution now done by computer algorithms. New high-tech trading venues, such as dark pools, also now play outsized roles in financial markets. A lot of the impacts of these developments are poorly understood. In the EU particularly, the introduction of the Markets in Financial Instruments Directive (MiFID) and advancements in technology have combined to unleash a dramatic transformation of European capital markets. In order to better understand the role of high-tech trading venues in the modern financial markets' trading environment generally and in the UK in particular, I conduct three studies investigating questions linked to the three major developments in financial markets over the past decade; these are algorithmic/high-frequency trading, market fragmentation and dark trading. In the first study, I examine the changing relationship between the price impact of block trades and informed trading, by considering this phenomenon within a high-frequency trading environment on intraday and inter-day bases. I find that the price impact of block trades is stronger during the first hour of trading; this is consistent with the hypothesis that information accumulates overnight during non-trading hours. Furthermore, private information is gradually incorporated into prices despite heightened trading frequency. Evidence suggests that informed traders exploit superior information across trading days, and stocks with lower transparency exhibit stronger information diffusion effects when traded in blocks, thus informed block trading facilitates price discovery. The second study exploits the regulatory differences between the US and the EU to examine the impact of market fragmentation on dimensions of market quality. Unlike the US's Regulation National Market System, the EU's MiFID does not impose a formal exchange trading linkage or guarantee a best execution price. This has raised concerns about consolidated market quality in increasingly fragmented European markets. The second study therefore investigates the impact of visible trading fragmentation on the quality of the London equity market and find a quadratic relationship between fragmentation and adverse selection costs. At low levels of fragmentation, order flow competition reduces adverse selection costs, improves market transparency and enhances market efficiency by reducing arbitrage opportunities. However, high levels of fragmentation increase adverse selection costs. The final study compares the impact of lit and dark venues' liquidity on market liquidity. I find that compared with lit venues, dark venues proportionally contribute more liquidity to the aggregate market. This is because dark pools facilitate trades that otherwise might not easily have occurred in lit venues when the spread widens and the limit order queue builds up. I also find that informed and algorithmic trading hinder liquidity creation in lit and dark venues, while evidence also suggests that stocks exhibiting low levels of informed trading across the aggregate market drive dark venues' liquidity contribution.

Diese Arbeit untersucht eine Reihe multiplikativer Preiseinflussmodelle für das Handeln in einer riskanten Anlage. Unser risikoneutraler Investor versucht seine zu erwartenden Handelserlöse zu maximieren. Zunächst modellieren wir den vorübergehende Preiseinfluss als deterministisches Funktional der Handelsstrategie. Wir stellen den Zusammenhang mit Limit-Orderbüchern her und besprechen die optimale Strategie zum Auf- bzw. Abbau einer Anlageposition bei a priori unbeschränkem Anlagehorizont. Anschließend lösen wir das Optimierungsproblem mit festem Anlagehorizon in zwei Schritten. Mittels Variationsrechnung lässt sich die freie Grenzefläche, die Kauf- und Verkaufsregionen trennt, als lokales Optimum identifizieren, was entscheidend für die Verifikation globaler Optimalität ist. Im zweiten Teil der Arbeit erweitern wir den zwischengeschalteten Markteinflussprozess um eine stochastische Komponente, wodurch optimale Strategien dynamisch an zufällige Liquiditätsschwankungen adaptieren. Wir bestimmen die optimale Liquidierungsstrategie im zeitunbeschränkten Fall als die reflektierende Lokalzeit, die den Markteinfluss unterhalb eines explizit beschriebenen nicht-konstanten Grenzlevels hält. Auch dieser Beweis kombiniert Variationsrechnung und direkten Methoden. Um nun eine Zeitbeschränkung zu ermöglichen, müssen wir Semimartingalstrategien zulassen. Skorochods M1-Toplogie ist der Schlüssel, um die Klasse der möglichen Strategien in einer umfangreichen Familie von Preiseinflussmodellen, welche sowohl additiven, als auch multiplikativen Preiseinfluss umfasst, mit deterministischer oder stochastischer Liquidität, eindeutig von endlichen Variations- auf allgemeine càdlàg Strategien zu erweitern. Nach Einführung proportionaler Transaktionskosten lösen wir das entsprechende eindimensionale freie Grenzproblem des optimalen unbeschränkten Handels und beleuchten mögliche Lösungsansätze für das Liquidierungsproblem, das mit dem Verkauf der letzten Anleihe endet. / In this thesis, we study a class of multiplicative price impact models for trading a single risky asset. We model price impact to be multiplicative so that prices are guaranteed to stay non-negative. Our risk-neutral large investor seeks to maximize expected gains from trading. We first introduce a basic variant of our model, wherein the transient impact is a deterministic functional of the trading strategy. We draw the connection to limit order books and give the optimal strategy to liquidate or acquire an asset position infinite time horizon. We then solve the optimization problem for finite time horizon two steps. Calculus of variations allows to identify the free boundary surface that separates buy and sell regions and moreover show its local optimality, which is a crucial ingredient for the verification giving (global) optimality. In the second part of the thesis, we add stochasticity to the auxiliary impact process. This causes optimal strategies to dynamically adapt to random changes in liquidity. We identify the optimal liquidation strategy in infinite horizon as the reflection local time which keeps the market impact process below an explicitly described non-constant free boundary level. Again the proof technique combines classical calculus of variations and direct methods. To now impose a time constraint, we need to admit semimartingale strategies. Skorokhod's M1 topology is key to uniquely extend the class of admissible controls from finite variation to general càdlàg strategies in a broad class of market models including multiplicative and additive price impact, with deterministic or stochastic liquidity. After introducing proportional transaction costs in our model, we solve the related one-dimensional free boundary problem of unconstrained optimal trading and highlight possible solution methods for the corresponding liquidation problem where trading stops as soon as all assets are sold.

Submitted by Carlos Barros (cfbarros@americastg.com) on 2015-09-01T13:02:06Z No. of bitstreams: 1 Dissertação - Carlos Felipe Barros.docx: 511698 bytes, checksum: 15dad3f7330f64c20af5761c41ea0ef2 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2015-09-01T15:48:20Z (GMT) No. of bitstreams: 1 Dissertação - Carlos Felipe Barros.docx: 511698 bytes, checksum: 15dad3f7330f64c20af5761c41ea0ef2 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2015-09-02T13:37:45Z (GMT) No. of bitstreams: 1 Dissertação - Carlos Felipe Barros.docx: 511698 bytes, checksum: 15dad3f7330f64c20af5761c41ea0ef2 (MD5) / Made available in DSpace on 2015-09-02T13:37:58Z (GMT). No. of bitstreams: 1 Dissertação - Carlos Felipe Barros.docx: 511698 bytes, checksum: 15dad3f7330f64c20af5761c41ea0ef2 (MD5) Previous issue date: 2013-05-29 / The objective of this paper is to estimate a dynamic market depth measure, called VNET, for Brazilian stocks using transactions data. VNET gauges the difference between the numbers of buyer- and seller-initiated trades within the time it takes for the stock price to change by at least a certain amount. It is a realized measure of liquidity for a given price deterioration, which one may track throughout the trading day to capture liquidity’s short-term dynamics. More specifically, we model the price duration using an autoregressive conditional duration (ACD) model. The predetermined nature of the ACD process is convenient because it makes it possible to forecast future changes in the liquidity of a stock. By identifying the best moment to buy or sell, the VNET is an excellent starting point for any optimal execution strategy. Our empirical findings indicate that the VNET measure of market depth depends on the bid-ask spread, volume traded, number of trades, and both expected and unexpected price durations. Finally, we also estimate the price impact of a trade by varying the increment in the definition of price duration. / O objetivo desse trabalho é encontrar uma medida dinâmica de liquidez de ações brasileiras, chamada VNET. Foram utilizados dados de alta frequência para criar um modelo capaz de medir o excesso de compras e vendas associadas a um movimento de preços. Ao variar no tempo, o VNET pode ser entendido como a variação da proporção de agentes informados em um modelo de informação assimétrica. Uma vez estimado, ele pode ser utilizado para prever mudanças na liquidez de uma ação. O VNET tem implicações práticas importantes, podendo ser utilizado por operadores como uma medida estocástica para identificar quais seriam os melhores momentos para operar. Gerentes de risco também podem estimar a deterioração de preço esperada ao se liquidar uma posição, sendo possível analisar suas diversas opções, servindo de base para otimização da execução. Na construção do trabalho encontramos as durações de preço de cada ação e as diversas medidas associadas a elas. Com base nos dados observa-se que a profundidade varia com ágio de compra e venda, com o volume negociado, com o numero de negócios, com a duração de preços condicional e com o seu erro de previsão. Os resíduos da regressão de VNET se mostraram bem comportados o que corrobora a hipótese de que o modelo foi bem especificado. Para estimar a curva de reação do mercado, variamos os intervalos de preço usados na definição das durações.

In dieser Arbeit untersuchen wir mathematische Modelle für Finanzmärkte mit einem großen Händler, dessen Handelsaktivitäten transienten Einfluss auf die Preise der Anlagen haben. Zuerst beschäftigen wir uns mit der Frage, wie die Handelserlöse des großen Händlers definiert werden sollen. Wir identifizieren die Erlöse zunächst für absolutstetige Strategien als nichtlineares Integral, in welchem sowohl der Integrand als der Integrator von der Strategie abhängen. Unserere Hauptbeiträge sind hier die Identifizierung der Skorokhod M1 Topologie als geeigneter Topologue auf dem Raum aller Strategien sowie die stetige Erweiterung der Definition für die Handelserlöse von absolutstetigen auf cadlag Kontrollstrategien. Weiter lösen wir ein Liquidierungsproblem in einem multiplikativen Modell mit Preiseinfluss, in dem die Liquidität stochastisch ist. Die optimale Strategie wird beschrieben durch die Lokalzeit für Reflektion einer Diffusion an einer nicht-konstanten Grenze. Um die HJB-Variationsungleichung zu lösen und Optimalität zu beweisen, wenden wir probabilistische Argumente und Methoden aus der Variationsrechnung an, darunter Laplace-Transformierte von Lokalzeiten für Reflektion an elastischen Grenzen. In der zweiten Hälfte der Arbeit untersuchen wir die Absicherung (Hedging) für Optionen. Der minimale Superhedging-Preis ist die Viskositätslösung einer semi-linearen partiellen Differenzialgleichung, deren Nichtlinearität von dem transienten Preiseinfluss abhängt. Schließlich erweitern wir unsere Analyse auf Hedging-Probleme in Märkten mit mehreren riskanten Anlagen. Stabilitätsargumente führen zu strukturellen Bedingungen, welche für ein arbitragefreies Modell mit wechselseitigem Preis-Impakt gelten müssen. Zudem ermöglichen es jene Bedingungen, die Erlöse für allgemeine Strategien unendlicher Variation in stetiger Weise zu definieren. Als Anwendung lösen wir das Superhedging-Problem in einem additiven Preis-Impakt-Modell mit mehreren Anlagen. / In this thesis we study mathematical models of financial markets with a large trader (price impact models) whose actions have transient impact on the risky asset prices. At first, we study the question of how to define the large trader's proceeds from trading. To extend the proceeds functional to general controls, we ask for stability in the following sense: nearby trading activities should lead to nearby proceeds. Our main contribution in this part is to identify a suitable topology on the space of controls, namely the Skorokhod M1 topology, and to obtain the continuous extension of the proceeds functional for general cadlag controls. Secondly, we solve the optimal liquidation problem in a multiplicative price impact model where liquidity is stochastic. The optimal control is obtained as the reflection local time of a diffusion process reflected at a non-constant free boundary. To solve the HJB variational inequality and prove optimality, we need a combination of probabilistic arguments and calculus of variations methods, involving Laplace transforms of inverse local times for diffusions reflected at elastic boundaries. In the second half of the thesis we study the hedging problem for a large trader. We solve the problem of superhedging for European contingent claims in a multiplicative impact model using techniques from the theory of stochastic target problems. The minimal superhedging price is identified as the unique viscosity solution of a semi-linear pde, whose nonlinearity is governed by the transient nature of price impact. Finally, we extend our consideration to multi-asset models. Requiring stability leads to strong structural conditions that arbitrage-free models with cross-impact should satisfy. These conditions turn out to be crucial for identifying the proceeds functional for a general class of strategies. As an application, the problem of superhedging with cross-impact in additive price impact models is solved.