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.