abstract: This dissertation examines six different models in the field of econophysics using interacting particle systems as the basis of exploration. In each model examined, the underlying structure is a graph G = (V , E ), where each x ∈ V represents an individual who is characterized by the number of coins in her possession at time t. At each time step t, an edge (x, y) ∈ E is chosen at random, resulting in an exchange of coins between individuals x and y according to the rules of the model. Random variables ξt, and ξt(x) keep track of the current configuration and number of coins individual x has at time t respectively. Of particular interest is the distribution of coins in the long run. Considered first are the uniform reshuffling model, immediate exchange model and model with saving propensity. For each of these models, the number of coins an individual can have is nonnegative and the total number of coins in the system is conserved for all time. It is shown here that the distribution of coins converges to the exponential distribution, gamma distribution and a pseudo gamma distribution respectively. The next two models introduce debt, however, the total number of coins again remains fixed. It is shown here that when there is an individual debt limit, the number of coins per individual converges to a shifted exponential distribution. Alternatively, when a collective debt limit is imposed on the whole population, a heuristic argument is given supporting the conjecture that the distribution of coins converges to an asymmetric Laplace distribution. The final model considered focuses on the effect of cooperation on a population. Unlike the previous models discussed here, the total number of coins in the system at any given time is not bounded and the process evolves in continuous time rather than in discrete time. For this model, death of an individual will occur if they run out of coins. It is shown here that the survival probability for the population is impacted by the level of cooperation along with how productive the population is as whole. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2019

Neste trabalho, fazemos uma breve introdução à Econofísica e às grandezas estatísticas relevantes para o estudo de um ativo financeiro. Estas grandezas são estudadas detalhadamente para o índice NYSE Composto. Determinamos o tempo de autocorrelação e o espectro de potência, cujos resultados indicam a presença de uma correlação de curto alcance. Através do expoente de Hurst, investigamos o tipo de correlação presente e detectamos a presença de multifractalidade. A volatilidade do índice NYSE mostrou-se análoga a um processo de Wiener. Por outro lado, a função densidade de probabilidade do índice NYSE foi ajustada por uma distribuição de Lévy simétrica com alpha = 1,47. Apresentamos os modelos de variância autoregressiva ARCH e GARCH. Em particular, focalizamos o modelo Markoviano GARCH(1,1). Este modelo tem três parâmetros de controle. Mostramos que, para o índice NYSE, o uso do tempo de autocorrelação na determinação deste conjunto de parâmetros de controle não é a melhor escolha. Resultados muito mais satisfatórios são obtidos se utilizarmos o sexto momento padronizado, uma vez que o ganho no ajuste da função de autocorrelação temporal é muito mais expressivo. A proposta de utilização do sexto momento é robusta e se aplica tanto ao modelo GARCH Gaussiano quanto ao modelo GARCH Exponencial. Desenvolvemos uma técnica de expansão em série para obter o sexto momento padronizado em função dos três parâmetros de controle. Obtivemos uma expressão analítica exata para a curtose do modelo GARCH Exponencial. Ambas as versões Gaussiana e Exponencial apresentam um desempenho equivalente na descrição da função densidade de probabilidade e da função de autocorrelação temporal. Porém, no que tange às leis de escala temporal, medidas através da probabilidade de retorno à origem, o modelo Exponencial tem, clara e inequivocamente, um melhor desempenho que o modelo Gaussiano, pois apresenta um expoente da lei de escala temporal em bom acordo com o expoente do índice NYSE. / In this thesis, we briefly give an introduction to Econophysics and discuss some important statistical quantities used in the study of a financial asset. This quantities are meticulously studied for the NYSE Composite Index. For its time series, we determine the time autocorrelation and the power spectrum, which show the presence of a short range correlation. By means of the Hurst exponent, we investigate the kind of autocorrelation which is present and we detected the presence of multifractality. The volatility of the NYSE Index show a behavior analogous to a Wiener process. On the other hand, the probability density function was adjusted by a symmetric Lévy distribuition with alpha = 1.47. We present the variance autoregressive ARCH and GARCH models. More specifically, we focus on the Markovian GARCH(1,1) model. This model has three control parameters. We show that, for the NYSE Index, the use of the time autocorrelation to determinate the set of control parameters is not the best choice. Instead, results much more reasonable are obtained if the standardized sixth moment is used, as can be seen by the adjust of the time autocorrelation function. The proposal of the sixth moment is robust and applies for both the Gaussian and the Exponential GARCH models. We developed a series expansion technique to get the standardized sixth moment as a function of the three control parameters. We found an exact analytic expression for the kurtosis of the Exponential GARCH model. Both the Gaussian and the Exponential versions exhibit an equivalent performance in the description of the probability density function and the time autocorrelation function. However, with respect to the time scaling laws (measured by the probability of return to the origin) the Exponential model shows, in a clear and unequivocal way, a better performance than the Gaussian model, since it gives a time horizon exponent much more close to the real NYSE exponent.

[pt] As flutuações de preços e de outras grandezas observáveis nos mercados financeiros apresentam comportamentos não triviais, tais como longas correlações temporais, não gaussianidade ou leis de escala, cuja origem não é ainda bem compreendida. Neste trabalho investigamos possíveis mecanismos determinísticos e estocásticos responsáveis pelas distribuições de probabilidade anômalas observadas para os índices de mercado e para os volumes de ações comercializadas. No primeiro caso, consideramos a expansão de Kramers-Moyal como ponto de partida para descrever a evolução das densidades de probabilidade. Para a modelagem dos volumes negociados, consideramos misturas estatísticas que surgem das flutuações em escalas longas dos parâmetros internos que descrevem a dinâmica em escalas mais curtas. Este estudo provê uma demonstração consistente, a partir de análise empírica de séries temporais reais, de como funções de densidade de probabilidade com caudas em lei de potência podem emergir através de mecanismos diversos, tais como processos estocásticos com flutuações aditivo-multiplicativas, ou como resultado de misturas estatísticas. / [en] The fluctuations of prices and other observables in financial markets have non-trivial behaviors, such as long temporal correlations, non-Gaussianity or scaling laws, whose origin is not well understood so far. In this work we have investigated possible deterministic and stochastic mechanisms responsible for the anomalous probability distributions observed for market indexes and volumes of traded shares. In the first case, we consider the Kramers-Moyal expansion as a starting point to describe the evolution of probability densities. For the modelling of trading volumes, we consider the mixed statistics that emerges from the long-scale fluctuations of inner parameters that describe the dynamics on shorter scales. This study provides a consistent demonstration, from empirical analysis of real time series, on how probability density functions with power laws tails may emerge through various mechanisms, such as stochastic processes with additive-multiplicative fluctuations or as a result of mixed statistics.

Neste trabalho, fazemos uma breve introdução à Econofísica e às grandezas estatísticas relevantes para o estudo de um ativo financeiro. Estas grandezas são estudadas detalhadamente para o índice NYSE Composto. Determinamos o tempo de autocorrelação e o espectro de potência, cujos resultados indicam a presença de uma correlação de curto alcance. Através do expoente de Hurst, investigamos o tipo de correlação presente e detectamos a presença de multifractalidade. A volatilidade do índice NYSE mostrou-se análoga a um processo de Wiener. Por outro lado, a função densidade de probabilidade do índice NYSE foi ajustada por uma distribuição de Lévy simétrica com alpha = 1,47. Apresentamos os modelos de variância autoregressiva ARCH e GARCH. Em particular, focalizamos o modelo Markoviano GARCH(1,1). Este modelo tem três parâmetros de controle. Mostramos que, para o índice NYSE, o uso do tempo de autocorrelação na determinação deste conjunto de parâmetros de controle não é a melhor escolha. Resultados muito mais satisfatórios são obtidos se utilizarmos o sexto momento padronizado, uma vez que o ganho no ajuste da função de autocorrelação temporal é muito mais expressivo. A proposta de utilização do sexto momento é robusta e se aplica tanto ao modelo GARCH Gaussiano quanto ao modelo GARCH Exponencial. Desenvolvemos uma técnica de expansão em série para obter o sexto momento padronizado em função dos três parâmetros de controle. Obtivemos uma expressão analítica exata para a curtose do modelo GARCH Exponencial. Ambas as versões Gaussiana e Exponencial apresentam um desempenho equivalente na descrição da função densidade de probabilidade e da função de autocorrelação temporal. Porém, no que tange às leis de escala temporal, medidas através da probabilidade de retorno à origem, o modelo Exponencial tem, clara e inequivocamente, um melhor desempenho que o modelo Gaussiano, pois apresenta um expoente da lei de escala temporal em bom acordo com o expoente do índice NYSE. / In this thesis, we briefly give an introduction to Econophysics and discuss some important statistical quantities used in the study of a financial asset. This quantities are meticulously studied for the NYSE Composite Index. For its time series, we determine the time autocorrelation and the power spectrum, which show the presence of a short range correlation. By means of the Hurst exponent, we investigate the kind of autocorrelation which is present and we detected the presence of multifractality. The volatility of the NYSE Index show a behavior analogous to a Wiener process. On the other hand, the probability density function was adjusted by a symmetric Lévy distribuition with alpha = 1.47. We present the variance autoregressive ARCH and GARCH models. More specifically, we focus on the Markovian GARCH(1,1) model. This model has three control parameters. We show that, for the NYSE Index, the use of the time autocorrelation to determinate the set of control parameters is not the best choice. Instead, results much more reasonable are obtained if the standardized sixth moment is used, as can be seen by the adjust of the time autocorrelation function. The proposal of the sixth moment is robust and applies for both the Gaussian and the Exponential GARCH models. We developed a series expansion technique to get the standardized sixth moment as a function of the three control parameters. We found an exact analytic expression for the kurtosis of the Exponential GARCH model. Both the Gaussian and the Exponential versions exhibit an equivalent performance in the description of the probability density function and the time autocorrelation function. However, with respect to the time scaling laws (measured by the probability of return to the origin) the Exponential model shows, in a clear and unequivocal way, a better performance than the Gaussian model, since it gives a time horizon exponent much more close to the real NYSE exponent.

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Yes / The link between finance and politics (especially opinion polling) is interesting in both theoretical and empirical terms. Inter alia the election date corresponds to the effective price of an underlying at a known future date. This renders a derivative pricing approach appropriate and, ultimately, to a simplification of the approach suggested by Taleb (2018). Thus, we use an options-pricing approach to predict vote share. Rather than systematic bias in polls forecasting errors appear chiefly due to the mode of extracting election outcomes from the share of the vote. In the 2016 US election polling results put the Republicans ahead in the electoral college from July 2016 onwards. In the 2017 UK general election, though set to be the largest party, a Conservative majority was far from certain.

Over the last decades, multifractality has become a downright stylized fact in financial markets. However, its presence has not been adequately statistically proved. The main aim of this thesis is to contribute to the discussion by an ex- tensive statistical analysis of the problem. We investigate returns and volatility of the collection of the four stock indices employing the three popular methods: the GHE, the MF-DFA, and the MF-DMA method. By comparing the results of the original series to those for simulated monofractal series, we conclude that stock market returns as well as volatility exhibit a multifractal nature. Additionally, in order to understand the origin of underlying multifractality, we study vari- ous surrogate series. We found that a fat-tailed distribution significantly affects multifractality. On the other, we were not able to confirm the impact of time correlations as the results strongly depend on the applied model. JEL Classification F12, G02, G10, C12, C22, C49, C58 Keywords econophysics, multifractality, financial markets, Hurst exponent Author's e-mail jana.sedlarikova@gmail.com Supervisor's e-mail kristoufek@ies-prague.org

[pt] Medida da magnitude de flutuação dos preços, a volatilidade é uma métrica importante para definir as estratégias de negociação e de controle de risco mais adequadas. Esse trabalho desenvolve um modelo de volatilidade fenomenológico baseado na rede microscópica heterogenea na qual os agentes especuladores respondem à chegada das informações. A dinâmica das características da volatilidade, modeladas por processos estocásticos, é governada por assimetrias no fluxo de informação através de diferentes resoluções temporais de análise. Entre essas características, destacamos os fatos estilizados de memória longa, clustering e efeito de alavancagem. Essas propostas são elucidadas através da análise empírica das séries de preço de um minuto do índice Ibovespa no período de dez anos. / [en] Volatility, as a metric for price uncertainty, is an important quantity for suitable trade strategy and risk control. This work develops a phenomenological volatility model based on a heterogeneous microstructure framework in which the market agents of speculative activity respond to information arrivals. The dynamic features of volatility, modeled as a stochastic process, is governed by asymmetries in the informational flow across different time resolutions. Among these features, we highlight the stylized facts of long memory, clustering and leverage effect. These proposals are contrasted with our empirical analysis of a ten-year time series of one-minute Brazilian market Index.

In the 1990s, physicists started looking beyond their disciplinary boundaries by using their methods to study various problems usually thrown up by financial economics. This dissertation deals with this extension of physics outside its disciplinary borders. It seeks to determine what sort of discipline econophysics is in relation to physics and to economics, how its emergence was made possible, and what sort of knowledge it produces. Using a variety of evidence including bibliometric analysis Chapter 1 explores the field’s disciplinary identity as a branch of physics even though its intellectual heart is better seen as the re-emergence of a 1960s research programme initiated in economics. Chapter 2 is historical: it identifies the key role played by the Santa Fe Institute and its pioneering complexity research in the shaping of methodological horizons of econophysics. These are in turn investigated in Chapter 3, which argues that there are in fact three methodological strands: statistical econophysics, bottom-up agent-based econophysics, and top-down agent-based econophysics. Viewed from a Lakatosian perspective they all share a conceptual hard-core but articulate the protective belt in distinctly different ways. The last and final chapter is devoted to the way econophysicists produce and justify their knowledge. It shows that econophysics operates by proposing empirically adequate analogies between physical and other systems in exactly the ways emphasised by Pierre Duhem. The contrast between such use of analogy in econophysics and modeling practices implemented by financial economics explains why econophysics remains so controversial to economists.

Made available in DSpace on 2017-07-21T19:25:57Z (GMT). No. of bitstreams: 1 ADRIANOPEREIRA.pdf: 5814518 bytes, checksum: fd0af0d5e0a77b57e48974063eac7e4f (MD5) Previous issue date: 2008-07-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Recurrence analysis has been extensively used in approaching problems that deal with transitions between regular and chaotic behaviors, identi¯cation of structure of dynamic systems, such as frequencies and correlations hard to detect by linear methods, for example. Among the main tools of this analysis are the Recurrence Plots (RP) and the Quantitative Recurrence Analysis (RQA), which are constantly used in the analysis of time series supposedly proceeding from non-linear and even non-stationary dynamical systems. These tools have been applied in a wide range of phenomena, since the study of cardiac arrhythmia until the greater phenomena of nature, such as sunspots. Recently, many economic and ¯financial séries are being investigated under this perspective, as exchange rates, the financial crashes" and the behavior of some stock index. In this work we employ the RP and RQA for the study of a long time series of the returns of the Bovespa Index (Ibovespa), where we carefully studied the obtention of the parameters for the phase space reconstruction of the supposed system which created the time series, we analyze the patterns formed in RP as well as the values of the quantities of RQA, comparing the results obtained with the original and randomized series. We search, from these results,to establish whether there is some sort of deterministic component in the studied system, and what its intensity. Our investigations suggest that the real financial market dynamics is a combination of deterministic chaos and stochastic behavior. / A análise da recorrência vem sendo muito usada na abordagem de problemas que tratam das transicões entre comportamentos regulares e caoticos, na identicação da estrutura de sistemas dinamicos, como frequências e correlacõess dificeis de detectar por metodos lineares, por exemplo. Dentre as principais ferramentas desta analise destacam-se os Gráficos de Recorrência (GR) e a Análise Quantitativa de Recorrência (AQR), que são constantemente empregadas na análise de séries temporais supostamente provenientes de sistemas dinâmicos não-lineares e até não-estacionários. Tais ferramentas vêm sendo aplicadas em uma grande gama de fenômenos, desde o estudo da arritmia cardíaca até os maiores fenômenos da natureza, como as manchas solares. Recentemente, muitas séries econômicas e financeiraso estão sendo investigadas sob esta ótica, como as taxas de cãmbio, os grandes crashes" financeiros e o comportamento de alguns índices de acões. Neste trabalho nós empregamos os GR e a AQR para o estudo de uma longa série temporal dos retornos do índice Bovespa (Ibovespa), onde estudamos cuidadosamente a obtencão dos parâmetros para a reconstrucão do suposto espaço de fase do sistema que gerou a série temporal, analisamos os padrões formados nos GR bem como os valores das quantidades da AQR, comparando os resultados obtidos com as séries originais e embaralhadas. Procuramos, a partir de tais resultados, estabelecer se existe algum tipo de componente determinística no sistema analisado, e qual sua intensidade. Nossas investigações sugeriram que a dinâmica real do mercado financeiro e uma combinacão de caos determinístico e comportamento estocástico.