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.

Foreign Capital and Finland : Central government's first period of reliance on international financial markets, 1862-1938

The main objective of the study is to evaluate the Finnish central government s foreign borrowing between the years 1862 and 1938. Most of this period was characterised by deep capital market integration that bears resemblance to the liberal world financial order at the turn of the millennium. The main aim is to analyse the credit risk associated with the state and its determination by evaluating the world financial market centres perception of Finland. By doing this, the study is also expected to provide an additional dimension to Finland s political and economic history by incorporating into the research the assessments of international capital markets regarding Finland during a period that witnessed profound political and economic changes in Finnish society. The evaluation of the credit risk mainly relies on exchange-rate risk free time series of the state s foreign bonds. They have been collected from quotations in the stock exchanges in Helsinki, Hamburg, Paris and London. In addition, it investigates Finland s exposure to short-term debt and Moody s credit ratings assigned to Finland. The study emphasises the importance of the political risk. It suggests that the hey-day of the state s reliance on foreign capital markets took place during last few decades of the 19th century when Finland enjoyed a wide autonomy in the Russian Empire and prudently managed its economy, highlighted in Finland s adherence to the international gold standard. Political confrontations in Finland and, in particular, in Russia and the turbulence of the world financial system prevented the return of this beneficial position again. Through its issuance of foreign bonds the state was able to import substantial amounts of foreign capital, which was sorely needed to foster economic development in Finland. Moreover, the study argues that the state s presence in the western capital markets not only had economic benefits, but it also increased the international awareness of Finland s distinct and separate status in the Russian Empire and later underlined its position as an independent republic.

Finnish and Austrian Wood Markets in a Changing Environment

At present the operating environment of sawmills in Europe is changing and there are uncertainties related in raw material supply in many countries. The changes in the operating environment of roundwood markets and the effects followed by these changes have brought up several interesting issues from the viewpoint of research. Lately new factors have been influencing the roundwood markets, such as increasing interest towards wood-based energy and implementation of new energy policies as well as changes in wood trade flows that affect the domestic markets in many countries. This Master’s thesis studies the adaptation ability of Finnish roundwood markets in a changing operating environment, aiming to produce an up-to-date analysis considering new development trends. The study concentrates on the roundwood markets from the viewpoint of sawmill industry since the industry is dependent on the functioning of the markets and sawmills are highly affected by the changes on the roundwood markets. To facilitate international comparison, the study is implemented by comparing Finnish and Austrian roundwood markets and analysing changes happening in the two countries. Finland and Austria share rather similar characteristics in the roundwood market structures, forest resources and forest ownership as well as production of roundwood and sawnwood. In addition they both are big exporters of forest industry products. In this study changes in the operating environment of sawmill industry both in Finland as well as in Austria are compared to each other aiming to recognise the main similarities and differences between the countries. In addition both development possibilities as well as challenges followed by the changes are discussed. The aim of the study is to define the main challenges and possibilities confronted by the actors on the markets and also to find new perspectives to approach these. The study is implemented as a qualitative study. The theoretical framework of the study describes the operating environment of wood markets from the viewpoint of the sawmill industry and represents the effects of supply and demand on the wood markets. The primary research material of the study was gathered by interviewing high level experts of forestry and sawmill industry in both Finland and Austria. The aim was to receive as extensive country specific viewpoint from the markets as possible, hence interviewees represented different parties of the markets. After creating country-specific profiles based on the theoretical framework a cross-country comparison was implemented. As a consequence the main similarities and differences in the operating environment and on the roundwood markets of Finland and Austria were recognized. In addition the main challenges and possibilites were identified. The results of the study offer a wide analysis regarding the main similarities and differences of the wood markets of Finland and Austria and their operating environments as well as concerning challenges and possibilities faced on the markets.

Finnish Short-Term Stock Returns

Functioning capital markets are a crucial part of a competitive economy since they provide the mechanisms to allocate resources. In order to be well functioning a capital market has to be efficient. Market efficiency is defined as a market where prices at any time fully reflect all available information. Basically, this means that abnormal returns cannot be predicted since they are dependent on future, presently unknown, information. The debate of market efficiency has been going on for several decades. Most academics today would probably agree that financial markets are reasonably efficient since virtually nobody has been able to achieve continuous abnormal positive returns. However, it is clear that a set of return anomalies exists, although they are apparently to small to enable substantial economic profit. Moreover, these anomalies can often be attributed to market design. The motivation for this work is to expand the knowledge of short-term trading patterns and to offer some explanations for these patterns. In the first essay the return pattern during the day is examined. On average stock prices move during two time periods of the day, namely, immediately after the opening and around the formal close of the market. Since stock prices, on average, move upwards these abnormal returns are generally positive and cause the distinct U-shape of intraday returns. In the second essay the results in the first essay are examined further. The return pattern around the former close is shown to partly be the result of manipulative action by market participants. In the third essay the focus is shifted towards trading patterns of the underlying stocks on days when index options and index futures on the stocks expire. Generally no expiration day effect was found. However, some indication of an expiration day effect was found when a large amount of open in- or at-the-money contracts existed. Also, the effects were likelier to be found for shares with high index-weight but fairly low trading volume. Last, in the forth essay the attention is turned to the behaviour of different tax clienteles around the dividend ex-day. Two groups of investors showed abnormal trading behaviour. Domestic non-financial investors, especially domestic companies, showed a dividend capturing behaviour, i.e. buying cum-dividend and selling ex-dividend shares. The opposite behaviour was found for foreign investors and domestic financial institutions. The effect was more notable for high yield, high volume stocks.

Intraday Dynamics of International Equity Markets

The increased availability of high frequency data sets have led to important new insights in understanding of financial markets. The use of high frequency data is interesting and persuasive, since it can reveal new information that cannot be seen in lower data aggregation. This dissertation explores some of the many important issues connected with the use, analysis and application of high frequency data. These include the effects of intraday seasonal, the behaviour of time varying volatility, the information content of various market data, and the issue of inter market linkages utilizing high frequency 5 minute observations from major European and the U.S stock indices, namely DAX30 of Germany, CAC40 of France, SMI of Switzerland, FTSE100 of the UK and SP500 of the U.S. The first essay in the dissertation shows that there are remarkable similarities in the intraday behaviour of conditional volatility across European equity markets. Moreover, the U.S macroeconomic news announcements have significant cross border effect on both, European equity returns and volatilities. The second essay reports substantial intraday return and volatility linkages across European stock indices of the UK and Germany. This relationship appears virtually unchanged by the presence or absence of the U.S stock market. However, the return correlation among the U.K and German markets rises significantly following the U.S stock market opening, which could largely be described as a contemporaneous effect. The third essay sheds light on market microstructure issues in which traders and market makers learn from watching market data, and it is this learning process that leads to price adjustments. This study concludes that trading volume plays an important role in explaining international return and volatility transmissions. The examination concerning asymmetry reveals that the impact of the positive volume changes is larger on foreign stock market volatility than the negative changes. The fourth and the final essay documents number of regularities in the pattern of intraday return volatility, trading volume and bid-ask spreads. This study also reports a contemporaneous and positive relationship between the intraday return volatility, bid ask spread and unexpected trading volume. These results verify the role of trading volume and bid ask quotes as proxies for information arrival in producing contemporaneous and subsequent intraday return volatility. Moreover, asymmetric effect of trading volume on conditional volatility is also confirmed. Overall, this dissertation explores the role of information in explaining the intraday return and volatility dynamics in international stock markets. The process through which the information is incorporated in stock prices is central to all information-based models. The intraday data facilitates the investigation that how information gets incorporated into security prices as a result of the trading behavior of informed and uninformed traders. Thus high frequency data appears critical in enhancing our understanding of intraday behavior of various stock markets’ variables as it has important implications for market participants, regulators and academic researchers.

Essays on the Linkages Between Financial Markets, and Risk Asymmetries (summary section only)

During the last few decades there have been far going financial market deregulation, technical development, advances in information technology, and standardization of legislation between countries. As a result, one can expect that financial markets have grown more interlinked. The proper understanding of the cross-market linkages has implications for investment and risk management, diversification, asset pricing, and regulation. The purpose of this research is to assess the degree of price, return, and volatility linkages between both geographic markets and asset categories within one country, Finland. Another purpose is to analyze risk asymmetries, i.e., the tendency of equity risk to be higher after negative events than after positive events of equal magnitude. The analysis is conducted both with respect to total risk (volatility), and systematic risk (beta). The thesis consists of an introductory part and four essays. The first essay studies to which extent international stock prices comove. The degree of comovements is low, indicating benefits from international diversification. The second essay examines the degree to which the Finnish market is linked to the “world market”. The total risk is divided into two parts, one relating to world factors, and one relating to domestic factors. The impact of world factors has increased over time. After 1993, when foreign investors were allowed to freely invest in Finnish assets, the risk level has been higher than previously. This was also the case during the economic recession in the beginning of the 1990’s. The third essay focuses on the stock, bond, and money markets in Finland. According to a trading model, the degree of volatility linkages should be strong. However, the results contradict this. The linkages are surprisingly weak, even negative. The stock market is the most independent, while the money market is affected by events on the two other markets. The fourth essay concentrates on volatility and beta asymmetries. Contrary to many international studies there are only few cases of risk asymmetries. When they occur, they tend to be driven by the market-wide component rather than the portfolio specific element.

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.

Short-term Price Behavior and the Effect of Foreign Investors in Finnish Equity Markets (summary section only)

As globalization and capital free movement has increased, so has interest in the effects of that global money flow, especially during financial crises. The concern has been that large global money flows will affect the pricing of small local markets by causing, in particular, overreaction. The purpose of this thesis is to contribute to the body of work concerning short-term under- and overreaction and the short-term effects of foreign investment flow in the small Finnish equity markets. This thesis also compares foreign execution return to domestic execution return. This study’s results indicate that short-term under- and overreaction occurs in domestic-buy portfolios (domestic net buying) rather than in foreign-buy portfolios. This under- and overreaction, however, is not economically meaningful after controlling for the bid-ask bounce effect. Based on this finding, one can conclude that foreign investors do not have a destabilizing effect in the short-term in the Finnish markets. Foreign activity affects short-term returns. When foreign investors are net buyers (sellers) there are positive (negative) market adjusted returns. Literature related to nationality and institutional effect leads us to expect these kind of results. These foreign flows are persistent at a 5 % to 21 % level and the persistence of foreign buy flow is higher than the foreign sell flow. Foreign daily trading execution is worse than domestic execution. Literature which quantifies foreign investors as liquidity demanders and literature related to front-running leads us to expect poorer foreign execution than domestic execution.

The expiration day effect of indexoptions and index futures on the underlying shares

This paper studies the effect of the expiration day of index options and futures on the trading volume, variance and price of the underlying shares. The data consists of all trades for the underlying shares in the FOX-index for expiration days during the period October 1995 to the mid of yer 1999. The main results seem to support the findings of Kan 2001, i.e. no manipulation on a larger scale. However, some indication of manipulation could be found if certain characteristics are favorable. These characteristics include: a) a large quantity of outstanding futures or at/in the money options contracts, b) there exists shares with high index weight but fairly low trading volume. Lastly, there is some indication that manipulation might be more popular towards the end of the examined time period.

Short-Horizon Asymmetric Mean-Reversion and Overreactions: Evidence from the Nordic Stock Markets

This paper examines the asymmetric behavior of conditional mean and variance. Short-horizon mean-reversion behavior in mean is modeled with an asymmetric nonlinear autoregressive model, and the variance is modeled with an Exponential GARCH in Mean model. The results of the empirical investigation of the Nordic stock markets indicates that negative returns revert faster to positive returns when positive returns generally persist longer. Asymmetry in both mean and variance can be seen on all included markets and are fairly similar. Volatility rises following negative returns more than following positive returns which is an indication of overreactions. Negative returns lead to increased variance and positive returns leads even to decreased variance.

Intraday Linkages across International Equity Markets

Utilizing concurrent 5-minute returns, the intraday dynamics and inter-market dependencies in international equity markets were investigated. A strong intraday cyclical autocorrelation structure in the volatility process was observed to be caused by the diurnal pattern. A major rise in contemporaneous cross correlation among European stock markets was also noticed to follow the opening of the New York Stock Exchange. Furthermore, the results indicated that the returns for UK and Germany responded to each other’s innovations, both in terms of the first and second moment dependencies. In contrast to earlier research, the US stock market did not cause significant volatility spillover to the European markets.

On the Importance of Mutual Fund Families in Emerging Markets

This study contributes to the mutual fund literature by looking at performance persistence on a fund family level, allowing for individual equity, bond and balanced funds to be included under single family umbrellas. The study is conducted on the emerging Finnish mutual fund market, an environment in which the importance of superior fund family teams is likely to be accentuated. Using both non–parametric and parametric tests we find robust evidence of performance persistence for the fund families. Persistence is particularly strong in the first half of the investigation period, which highlights the importance of fund families at early stages of market development.