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.

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.

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 Labor Market Frictions, Technological Change and Macroeconomic Fluctuations

The dissertation consists of an introductory chapter and three essays that apply search-matching theory to study the interaction of labor market frictions, technological change and macroeconomic fluctuations. The first essay studies the impact of capital-embodied growth on equilibrium unemployment by extending a vintage capital/search model to incorporate vintage human capital. In addition to the capital obsolescence (or creative destruction) effect that tends to raise unemployment, vintage human capital introduces a skill obsolescence effect of faster growth that has the opposite sign. Faster skill obsolescence reduces the value of unemployment, hence wages and leads to more job creation and less job destruction, unambiguously reducing unemployment. The second essay studies the effect of skill biased technological change on skill mismatch and the allocation of workers and firms in the labor market. By allowing workers to invest in education, we extend a matching model with two-sided heterogeneity to incorporate an endogenous distribution of high and low skill workers. We consider various possibilities for the cost of acquiring skills and show that while unemployment increases in most scenarios, the effect on the distribution of vacancy and worker types varies according to the structure of skill costs. When the model is extended to incorporate endogenous labor market participation, we show that the unemployment rate becomes less informative of the state of the labor market as the participation margin absorbs employment effects. The third essay studies the effects of labor taxes on equilibrium labor market outcomes and macroeconomic dynamics in a New Keynesian model with matching frictions. Three policy instruments are considered: a marginal tax and a tax subsidy to produce tax progression schemes, and a replacement ratio to account for variability in outside options. In equilibrium, the marginal tax rate and replacement ratio dampen economic activity whereas tax subsidies boost the economy. The marginal tax rate and replacement ratio amplify shock responses whereas employment subsidies weaken them. The tax instruments affect the degree to which the wage absorbs shocks. We show that increasing tax progression when taxation is initially progressive is harmful for steady state employment and output, and amplifies the sensitivity of macroeconomic variables to shocks. When taxation is initially proportional, increasing progression is beneficial for output and employment and dampens shock responses.

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 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.

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.

Value Creation in Professional Service Processes. Propositions for Understanding Financial Value from a Customer Perspective

Many service management studies have suggested that service providers benefit from having long-term relationships with customers, but the argument from a customer perspective has been vague. However, especially in the business-to-business context, an analysis of financial value creation seems appropriate also from a customer perspective. Hence, the aim of this study is to develop a framework for understanding monetary value creation in professional service assignments from a customer perspective. The contribution of this study is an improved insight and framework for understanding financial value creation from a customer perspective in a professional service delivery process. The sources for monetary differences between transactional and long-term service providers are identified and quantified in case settings. This study contributes to the existing literature in service and relationship management by extending the customer’s viewpoint from perceived value to measurable monetary value. The contribution to the professional services lies in the process focus as opposed to the outcome focus, which is often accentuated in the existing professional services literature. The findings from the qualitative data suggest that a customer company may benefit from having an improved understanding of the service delivery (service assignment) process and the factors affecting the monetary value creation during the process. It is suggested that long-term relationships with service providers create financial value in the case settings in the short term. The findings also indicate that by using the improved understanding, a customer company can make more informed decisions when selecting a service provider for a specific assignment. Mirel Leino is associated with CERS, the Center for Relationship Marketing and Service Management at the Swedish School of Economics and Business Administration

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.

Bootstrap and Fast Double Bootstrap Tests of Cointegration Rank with Financial Time Series

The likelihood ratio test of cointegration rank is the most widely used test for cointegration. Many studies have shown that its finite sample distribution is not well approximated by the limiting distribution. The article introduces and evaluates by Monte Carlo simulation experiments bootstrap and fast double bootstrap (FDB) algorithms for the likelihood ratio test. It finds that the performance of the bootstrap test is very good. The more sophisticated FDB produces a further improvement in cases where the performance of the asymptotic test is very unsatisfactory and the ordinary bootstrap does not work as well as it might. Furthermore, the Monte Carlo simulations provide a number of guidelines on when the bootstrap and FDB tests can be expected to work well. Finally, the tests are applied to US interest rates and international stock prices series. It is found that the asymptotic test tends to overestimate the cointegration rank, while the bootstrap and FDB tests choose the correct cointegration rank.

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.

The Power of Bootstrap Tests of Cointegration Rank with Financial Time Series

Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of the correspond- ing asymptotic tests. The e¤ect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymp- totic test. The bootstrap test estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.