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.

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.

Cobreaking of Stock Prices and Contagion

Financial crises have shown that dramatic movements in one financial market can have a powerful impact on other markets. The paper proposes to use cobreaking to model comovements between financial markets during crises and to test for conta-gion. It finds evidence of cobreaking between stock returns in developed markets. Finding cobreaking has implications for the diversification of international investments. For emerging mar-ket stock returns the evidence of cobreaking is mainly due to the non-financial event of the 9/11 terrorist attacks in 2001. Fi-nancial crises originating in one emerging market do not spread to other markets, i.e., no contagion.

Modeling Asymmetries in Financial Data with Multiplicative Error Models

This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

Monetary Policy Implementation in the Interbank Market

The liquidity crisis that swept through the financial markets in 2007 triggered multi-billion losses and forced buyouts of some large banks. The resulting credit crunch is sometimes compared to the great recession in the early twentieth century. But the crisis also serves as a reminder of the significance of the interbank market and of proper central bank policy in this market. This thesis deals with implementation of monetary policy in the interbank market and examines how central bank tools affect commercial banks' decisions. I answer the following questions: • What is the relationship between the policy setup and interbank interest rate volatility? (averaging reserve requirement reduces the volatility) • What can explain a weak relationship between market liquidity and the interest rate? (high reserve requirement buffer) • What determines banks' decisions on when to satisfy the reserve requirement? (market frictions) • How did the liquidity crisis that began in 2007 affect interbank market behaviour? (resulted in higher credit risk and trading frictions as well as expected liquidity shortage)

Essays on Stock Market Reactions to New Information

A functioning stock market is an essential component of a competitive economy, since it provides a mechanism for allocating the economy’s capital stock. In an ideal situation, the stock market will steer capital in a manner that maximizes the total utility of the economy. As prices of traded stocks depend on and vary with information available to investors, it is apparent that information plays a crucial role in a functioning stock market. However, even though information indisputably matters, several issues regarding how stock markets process and react to new information still remain unanswered. The purpose of this thesis is to explore the link between new information and stock market reactions. The first essay utilizes new methodological tools in order to investigate the average reaction of investors to new financial statement information. The second essay explores the behavior of different types of investors when new financial statement information is disclosed to the market. The third essay looks into the interrelation between investor size, behavior and overconfidence. The fourth essay approaches the puzzle of negative skewness in stock returns from an altogether different angle than previous studies. The first essay presents evidence of the second derivatives of some financial statement signals containing more information than the first derivatives. Further, empirical evidence also indicates that some of the investigated signals proxy risk while others contain information priced with a delay. The second essay documents different categories of investors demonstrating systematical differences in their behavior when new financial statement information arrives to the market. In addition, a theoretical model building on differences in investor overconfidence is put forward in order to explain the observed behavior. The third essay shows that investor size describes investor behavior very well. This finding is predicted by the model proposed in the second essay, and hence strengthens the model. The behavioral differences between investors of different size furthermore have significant economic implications. Finally, the fourth essay finds strong evidence of management news disclosure practices causing negative skewness in stock returns.

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.

Corporate Funding on the European Debt Capital Market

The integrated European debt capital market has undoubtedly broadened the possibilities for companies to access funding from the public and challenged investors to cope with an ever increasing complexity of its market participants. Well into the Euro-era, it is clear that the unified market has created potential for all involved parties, where investment opportunities are able to meet a supply of funds from a broad geographical area now summoned under a single currency. Europe’s traditionally heavy dependency on bank lending as a source of debt capital has thus been easing as corporate residents are able to tap into a deep and liquid capital market to satisfy their funding needs. As national barriers eroded with the inauguration of the Euro and interest rates for the EMU-members converged towards over-all lower yields, a new source of debt capital emerged to the vast majority of corporate residents under the new currency and gave an alternative to the traditionally more maturity-restricted bank debt. With increased sophistication came also an improved knowledge and understanding of the market and its participants. Further, investors became more willing to bear credit risk, which opened the market for firms of ever lower creditworthiness. In the process, the market as a whole saw a change in the profile of issuers, as non-financial firms increasingly sought their funding directly from the bond market. This thesis consists of three separate empirical studies on how corporates fund themselves on the European debt capital markets. The analysis focuses on a firm’s access to and behaviour on the capital market, subsequent the decision to raise capital through the issuance of arm’s length debt on the bond market. The specific areas considered are contributing to our knowledge in the fields of corporate finance and financial markets by considering explicitly firms’ primary market activities within the new market area. The first essay explores how reputation of an issuer affects its debt issuance. Essay two examines the choice of interest rate exposure on newly issued debt and the third and final essay explores pricing anomalies on corporate debt issues.

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.

New Evidence on the Properties of the Financial Statement Information Pricing Process

This study contributes to our knowledge of how information contained in financial statements is interpreted and priced by the stock market in two aspects. First, the empirical findings indicate that investors interpret some of the information contained in new financial statements in the context of the information of prior financial statements. Second, two central hypotheses offered in earlier literature to explain the significant connection between publicly available financial statement information and future abnormal returns, that the signals proxy for risk and that the information is priced with a delay, are evaluated utilizing a new methodology. It is found that the mentioned significant connection for some financial statement signals can be explained by that the signals proxy for risk and for other financial statement signals by that the information contained in the signals is priced with a delay.

How Do Different Types of Investors React to New Financial Statement Information?

The study contributes to our understanding of the forces that drive the stock market by investigating how different types of investors react to new financial statement information. Using the extremely comprehensive official register of share holdings in Finland, we find that the majority of investors are more probable to sell (buy) stocks in a company after a positive (negative) earnings surprise, and show a bias towards buying after the disclosure of new financial statement information. Large investors, on the other hand, show behavior opposite to that of the majority of investors in the market. Further, foreign investors show behavior similar to that of domestic investors. We suggest investor overconfidence and asymmetric information as possible explanations for the documented behavior.