published_or_final_version / abstract / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

Several models in econometrics and finance have been proven to be computationally intractable due to their complexity. In this dissertation, we propose an evolutionary-genetic-algorithm for solving these types of problems. We extend the models so that less restrictive assumptions are required and we cope with the increased complexity by using a modified version of the evolutionary algorithm proposed for the simpler cases. More specifically, we study closer the estimation of switching regression models as introduced by Quandt (1958). The applicability of the proposed algorithms is examined through disequilibrium models; models that provide supply and demand functions for markets, when the price is not adjusted so that the quantity supplied equals the quantity demanded. We focus on the computational aspect of the deterministic switching regression models and we suggest a self-evolving genetic algorithm for solving these types of problems. As an illustration, we present results from Monte Carlo simulations and thereafter we apply the algorithm to the disequilibrium model proposed for the gasoline market during the “energy crisis”. We further extend the “general model” for markets in disequilibrium by incorporating dynamic relationships, and we examine the applicability of the proposed genetic algorithm in this more complex and realistic problem. Subsequently, the proposed genetic algorithm for the markets in disequilibrium is applied to financial models, where the structure and computational complexity are comparable with those of the switching regression models. As example, we apply the algorithm to minimizing portfolio tracking error with respect to a pre-specified index. The proposed genetic algorithm possesses unique characteristics that maximize the fitness of the algorithm itself for each individual problem. This is achieved through a Self-Evolving process that teaches the genetic algorithm what internal parameters improve the algorithm's fitness.

Investors and financial analysts spend an inordinate amount of time, resources and effort in an attempt to perfect the science of maximising the level of financial returns. To this end, the field of distribution modelling and analysis of firm size effect is important as an investment analysis and appraisal tool. Numerous studies have been conducted to determine which distribution best fits stock returns (Mandelbrot, 1963; Fama, 1965 and Akgiray and Booth, 1988). Analysis and review of earlier research has revealed that researchers claim that the returns follow a normal distribution. However, the findings have not been without their own limitations in terms of the empirical results in that many also say that the research done does not account for the fat tails and skewness of the data. Some research studies dealing with the anomaly of firm size effect have led to the conclusion that smaller firms tend to command higher returns relative to their larger counterparts with a similar risk profile (Banz, 1981). Recently, Janse van Rensburg et al. (2009a) conducted a study in which both non- normality of stock returns and firm size effect were addressed simultaneously. They used a scale mixture of two normal distributions to compare the stock returns of large capitalisation and small capitalisation shares portfolios. The study concluded that in periods of high volatility, the small capitalisation portfolio is far more risky than the large capitalisation portfolio. In periods of low volatility they are equally risky. Janse van Rensburg et al. (2009a) identified a number of limitations to the study. These included data problems, survivorship bias, exclusion of dividends, and the use of standard statistical tests in the presence of non-normality. They concluded that it was difficult to generalise findings because of the use of only two (limited) portfolios. In the extension of the research, Janse van Rensburg (2009b) concluded that a scale mixture of two normal distributions provided a more superior fit than any other mixture. The scope of this research is an extension of the work by Janse van Rensburg et al. (2009a) and Janse van Rensburg (2009b), with a view to addressing several of the limitations and findings of the earlier studies. The Janse van rensburg (2009b) study was based on data from the Johannesburg Stock Exchange (JSE); this study seeks to compare their research by looking at the New York Stock Exchange (NYSE) to determine if similar results occur in developed markets. For analysis purposes, this study used the statistical software package R (R Development Core Team 2008) and its package mixtools (Young, Benaglia, Chauveau, Elmore, Hettmansperg, Hunter, Thomas, Xuan 2008). Some computation was also done using Microsoft Excel. This dissertation is arranged as follows: Chapter 2 is a literature review of some of the baseline studies and research that supports the conclusion that earlier research finding had serious limitations. Chapter 3 describes the data used in the study and gives a breakdown of portfolio formation and the methodology used in the study. Chapter 4 provides the statistical background of the methods used in this study. Chapter 5 presents the statistical analysis and distribution fitting of the data. Finally, Chapter 6 gives conclusions drawn from the results obtained in the analysis of data as well as recommendations for future work.

This thesis studies the problems of semistatic trading strategies in a discrete-time financial market, where stocks are traded dynamically and European options at maturity are traded statically. First, we show that pointwise limits of semistatic trading strategies are again semistatic strategies. The analysis is carried out in full generality for a two-period model, and under a probabilistic condition for multi-period, multi-stock models. Our result contrasts with a counterexample of Acciaio, Larsson and Schachermayer, and shows that their observation is due to a failure of integrability rather than instability of the semistatic form. Mathematically, our results relate to the decomposability of functions as studied in the context of Schrödinger bridges. Second, we study the so-called martingale Schrödinger bridge 𝑄⁎ in a two-period financial market; that is, the minimal-entropy martingale measure among all models calibrated to option prices. This minimization is shown to be in duality with an exponential utility maximization over semistatic portfolios. Under a technical condition on the physical measure 𝑃, we show that an optimal portfolio exists and provides an explicit solution for 𝑄⁎. Specifically, we exhibit a dense subset of calibrated martingale measures with particular properties to show that the portfolio in question has a well-defined and integrable option position.

Following the recent financial crisis, financial regulators have placed a strong emphasis on reducing expectations of government support for banks, and on better managing and assessing risks in the banking system. This thesis considers three current topics in credit risk and the statistical problems that arise there. The first of these topics is expectations of government support in distressed banks. We utilize unique features of the European credit default swap market to find that market expectations of European government support for distressed banks have decreased -- an important development in the credibility of financial reforms. The second topic we treat is the estimation of covariance matrices from the perspective of market risk management. This problem arises, for example, in the central clearing of credit default swaps. We propose several specialized loss functions, and a simple but effective visualization tool to assess estimators. We find that proper regularization significantly improves the performance of dynamic covariance models in estimating portfolio variance. The third topic we consider is estimation risk in the pricing of financial products. When parameters are not known with certainty, a better informed counterparty may strategically pick mispriced products. We discuss how total estimation risk can be minimized approximately. We show how a premium for remaining estimation risk may be determined when one counterparty is better informed than the other, but a market collapse is to be avoided, using a simple example from loan pricing. We illustrate the approach with credit bureau data.

Orientadores: Mauricio Enrique Zevallos Herencia, Luiz Koodi Hotta / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-14T12:07:35Z (GMT). No. of bitstreams: 1 Martim_SimoniFernanda_M.pdf: 2441806 bytes, checksum: 4d34450ac590270c90e7eb66a293b51b (MD5) Previous issue date: 2009 / Resumo: O diagnóstico de modelos é uma etapa fundamental para avaliar a qualidade do ajuste dos modelos. Nesse sentido, uma das ferramentas de diagnóstico mais importantes é a análise de influência. Peña (2005) introduziu uma forma de analisar a influência em modelos de regressão, a qual avalia como cada ponto é influenciado pelos outros na amostra. Essa estratégia de diagnóstico foi adaptada por Hotta e Motta (2007) na análise de influência dos modelos de volatilidade estocástica univariados. Nesta dissertação, é realizado um estudo de diagnóstico de influência para modelos de volatilidade estocástica univariados assimétricos, assim como para modelos de volatilidade estocástica multivariados. As metodologias propostas são ilustradas através da análise de dados simulados e séries reais de retornos financeiros. / Abstract: Model diagnostics is a key step to assess the quality of fitted models. In this sense, one of the most important tools is the analysis of influence. Peña (2005) introduced a way of assessing influence in linear regression models, which evaluates how each point is influenced by the others in the sample. This diagnostic strategy was adapted by Hotta and Motta (2007) on the influence analysis of univariate stochastic volatility models. In this dissertation, it is performed a study of influence diagnostics of asymmetric univariate stochastic volatility models as well as multivariate stochastic volatility models. The proposed methodologies are illustrated through the analysis of simulated data and financial time series returns. / Mestrado / Series Temporais Financeiras / Mestra em Estatística

Partnerships of private and public sectors in form of so-called PPP can be assumed for modern and efficient instrument for public services provision under certain conditions. Its optimal functioning is connected with many assumptions -- for example rigorous implementation of value of money concept and complying with international best practice together with national specifics reflection. Key aspect of PPP is risk allocation which is also the main generator of abovementioned value for money. The paper pursues to PPP definition, its basic types, principles, advantages and potential threats. The emphasis is put on identification, reflection and management of risks in PPP framework, which can be connected with lower level of transparency and many hampers for reliable value for money achievement demonstration (in comparison with classic public procurement). Paper tries to illustrate main features of the most common methods used for risk adjustment in PPP. There are used and described methods coming from Victoria Partnership, MFSR and Treasury UK methodologies. The most important parameters of financial model used for investment decision-making and following project management and their specificities in the Czech Republic are mentioned. Separate chapter of diploma paper is devoted to PPP recording in government finance statistics and government and debt impacts especially in ESA 95 and GFSM 2001 methodologies. Also issues connected with PPP recording in government and financial crisis are mentioned. The final part of paper illustrates main features of the actual largest considered project D3/R3.

The analysis of the government sector gained prominence after the World War II as the Keynesian theory attributed the government sector key importance in battling economic cycle and the post-war reconstruction and development involved state interventions on a large scale. In 1990s a strength-ened interest in the government sector was triggered by the need to coordinate fiscal policies and closely monitor fiscal health in the countries forming the Economic and Monetary Union. Finally, in the context of the recent global economic crisis, the government sector returned to the centre of the economic policy debate as fiscal policy was used as a main tool to fight the economic recession and subsequently sustainability of government finances became a pressing issue for many countries around the Globe. Increasing importance of the fiscal analysis and fiscal policymaking always generated and continues to generate demand for appropriate statistical data. The international statistical standards played a key role in meeting these requirements. This dissertation offers a comprehensive historical overview, a comparative analysis and evaluation of main internationally recognised statistical standards dealing with the government sector produced by the United Nations, the OECD, the European Communities (Eurostat), the IMF and the European Central Bank. It covers a period since the first international guidelines in late 1940s up to present. It analyses evolution of the statistical treatment of the government sector including its historical roots and gradual revisions and extensions to reflect changing needs and shifts in economic environment. The study compares individual standards with each other and across time and points out differences in basic definitions, concepts and classifications, the institutional coverage of the government sector, structure of government accounts and balancing items, integration of flow accounts with balance sheets and consolidation of transactions or stocks. The dissertation shows that the international statistical standards were successful in offering common statistical guidance, recommendations and best practices. The international organizations have proven to be well suited to deliver widely acknowledged standards. Their cooperation with national statistical agencies and engagement of the most competent experts in the field contributed to building credibility of these statistical systems, if properly applied. The comparative analysis also demonstrates a clear long-term effort of the international statistical community to enhance international harmonization. The application of the international statistical standards also improved quality and availability of government statistics as individual countries are in principle bound -- through their memberships in the international organizations -- to compile agreed data on the basis of a common methodology. This was in particular the case for EU countries for which provision of statistical data according to a given standard is legally binding, as the data are relevant for budgetary and surveillance procedures. As a special case, the history since early 1990s and current situation of statistics on the government sector in the Czech Republic is presented.