Mathematical Aspects of Financial Markets with Frictions

Frictions are factors that hinder trading of securities in financial markets. Typical frictions include limited market depth, transaction costs, lack of infinite divisibility of securities, and taxes. Conventional models used in mathematical finance often gloss over these issues, which affect almost all financial markets, by arguing that the impact of frictions is negligible and, consequently, the frictionless models are valid approximations. This dissertation consists of three research papers, which are related to the study of the validity of such approximations in two distinct modeling problems. Models of price dynamics that are based on diffusion processes, i.e., continuous strong Markov processes, are widely used in the frictionless scenario. The first paper establishes that diffusion models can indeed be understood as approximations of price dynamics in markets with frictions. This is achieved by introducing an agent-based model of a financial market where finitely many agents trade a financial security, the price of which evolves according to price impacts generated by trades. It is shown that, if the number of agents is large, then under certain assumptions the price process of security, which is a pure-jump process, can be approximated by a one-dimensional diffusion process. In a slightly extended model, in which agents may exhibit herd behavior, the approximating diffusion model turns out to be a stochastic volatility model. Finally, it is shown that when agents' tendency to herd is strong, logarithmic returns in the approximating stochastic volatility model are heavy-tailed. The remaining papers are related to no-arbitrage criteria and superhedging in continuous-time option pricing models under small-transaction-cost asymptotics. Guasoni, Rásonyi, and Schachermayer have recently shown that, in such a setting, any financial security admits no arbitrage opportunities and there exist no feasible superhedging strategies for European call and put options written on it, as long as its price process is continuous and has the so-called conditional full support (CFS) property. Motivated by this result, CFS is established for certain stochastic integrals and a subclass of Brownian semistationary processes in the two papers. As a consequence, a wide range of possibly non-Markovian local and stochastic volatility models have the CFS property.

Essays on Market Microstructure: Price Discovery and Informed Trading

Market microstructure is “the study of the trading mechanisms used for financial securities��� (Hasbrouck (2007)). It seeks to understand the sources of value and reasons for trade, in a setting with different types of traders, and different private and public information sets. The actual mechanisms of trade are a continually changing object of study. These include continuous markets, auctions, limit order books, dealer markets, or combinations of these operating as a hybrid market. Microstructure also has to allow for the possibility of multiple prices. At any given time an investor may be faced with a multitude of different prices, depending on whether he or she is buying or selling, the quantity he or she wishes to trade, and the required speed for the trade. The price may also depend on the relationship that the trader has with potential counterparties. In this research, I touch upon all of the above issues. I do this by studying three specific areas, all of which have both practical and policy implications. First, I study the role of information in trading and pricing securities in markets with a heterogeneous population of traders, some of whom are informed and some not, and who trade for different private or public reasons. Second, I study the price discovery of stocks in a setting where they are simultaneously traded in more than one market. Third, I make a contribution to the ongoing discussion about market design, i.e. the question of which trading systems and ways of organizing trading are most efficient. A common characteristic throughout my thesis is the use of high frequency datasets, i.e. tick data. These datasets include all trades and quotes in a given security, rather than just the daily closing prices, as in traditional asset pricing literature. This thesis consists of four separate essays. In the first essay I study price discovery for European companies cross-listed in the United States. I also study explanatory variables for differences in price discovery. In my second essay I contribute to earlier research on two issues of broad interest in market microstructure: market transparency and informed trading. I examine the effects of a change to an anonymous market at the OMX Helsinki Stock Exchange. I broaden my focus slightly in the third essay, to include releases of macroeconomic data in the United States. I analyze the effect of these releases on European cross-listed stocks. The fourth and last essay examines the uses of standard methodologies of price discovery analysis in a novel way. Specifically, I study price discovery within one market, between local and foreign traders.

Essays on Financial Analyst Forecasts and Recommendations

The trade of the financial analyst is currently a much-debated issue in today’s media. As a large part of the investment analysis is conducted under the broker firms’ regime, the incentives of the financial analyst and the investor do not always align. The broker firm’s commercial incentives may be to maximise its commission from securities trading and underwriting fees. The purpose of this thesis is to extend our understanding of the work of a financial analyst, the incentives he faces and how these affect his actions. The first essay investigates how the economic significance of the coverage of a particular firm impacts the analysts’ accuracy of estimation. The hypothesis is that analysts put more effort in analysing firms with a relatively higher trading volume, as these firms usually yield higher commissions. The second essay investigates how analysts interpret new financial statement information. The essay shows that analysts underreact or overreact to prior reported earnings, depending on the short-term pattern in reported earnings. The third essay investigates the possible investment value in Finnish stock recommendations, issued by sell side analysts. It is established that consensus recommendations issued on Finnish stocks contain investment value. Further, the investment value in consensus recommendations improves significantly through the exclusion of recommendations issued by banks. The fourth essay investigates investors’ behaviour prior to financial analysts’ earnings forecast revisions. Lately, the financial press have reported cases were financial analysts warn their preferred clients of possible earnings forecast revisions. However, in the light of the empirical results, it appears that the problem of analysts leaking information to some selected customers does not appear systematically on the Finnish stock market.

The Relationship Between Liquidity, Trading Activity and Return - Studies of the Finnish and Swedish Stock Markets

Liquidity, or how easy an investment is to buy or sell, is becoming increasingly important for financial market participants. The objective of this dissertation is to contribute to the understanding of how liquidity affects financial markets. The first essays analyze the actions taken by underwriters immediately after listing to improve liquidity of IPO stock. To estimate the impact of underwriter activity on the pricing of the IPOs, the order book during the first weeks of trading in the IPO stock is studied. Evidence of stabilization and liquidity enhancing activities by underwriters is found. The second half of the dissertation is concerned with the daily trading of stocks where liquidity may be impacted by policy issues such as changes in taxes or exchange fees and by opening the access to the markets for foreign investors. The desirability of a transaction tax on securities trading is addressed. An increase in transaction tax is found to cause lower prices and higher volatility. In the last essay the objective is to determine if the liquidity of a security has an impact on the return investors require. The results support the notion that returns are negatively correlated to liquidity.