Title: Option Pricing Author: Radek Moravec Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathematical Statistics In the present thesis we deal with European call option pricing using lattice approaches. We introduce a discrete market model and show a way how to find an arbitrage price of financial instruments on complete markets. It's equal to the discounted value of future expected cash flow. We present the binomial option pricing model and generalize it into multinomial model. We test the resulting formula on real market data obtained from NYSE and NASDAQ. We suggest a parameter estimate method which is based on time series of historical observations of daily close price. We compare calculated option prices with their real market value and try to explain the reasons of the differences. 1

The Slovenian Public Opinion survey (SPOS), which carried out in 1990, was used by the government of Slovenia as a benchmark to prepare for an upcoming plebiscite, which asked the respondents whether they support independence from Yugoslavia. However, the sample size was large and it is quite likely that the respondents and nonrespondents had divergent viewpoints. We first develop an ignorable nonresponse model which is an extension of a bivariate binomial model. In order to accommodate the nonrespondents, we then develop a nonignorable nonresponse model which is an extension of the ignorable model. Our methodology uses an EM algorithm to fit both the ignorable and nonignorable nonresponse models, and estimation is carried out using the bootstrap mechanism. We also perform sensitivity analysis to study different degrees of departures of the nonignorable nonresponse model from the ignorable nonresponse model. We found that the nonignorable nonresponse model is mildly sensitive to departures from the ignorable nonresponse model. In fact, our finding based on the nonignorable model is better than an earlier conclusion about another nonignorable nonresponse model fitted to these data.

This thesis is focused on sentiment analysis of unstructured text and its practical application on the real data downloaded from website Yelp.com The objectives of the theoretical part of this thesis is to sum up the information related to history, methods and possible applications of sentiment analysis. A reader is acquainted with important terms and processes of sentiment analysis. Theoretical part is focused on Naive Bayes classifier, that will be used in practical part of this thesis. In practical part there is detailed description of data set, construction and testing of model. At the end there are presented pros and cons of the chosen model and described some possibilities of its usage.

Le premier chapitre, écrit conjointement avec Alfred Galichon, Keith O'Hara et Matthew Shum, montre l'équivalence entre les modèles de choix discrets et les modèles d'appariements. Cette équivalence permet l'estimation efficace, par des algorithmes d'appariement, de modèles qui étaient jusqu'à présent réputés comme difficile à estimer dans la littérature. Le deuxième chapitre, écrit conjointement avec Mathilde Poulhès, s'appuie sur les résultats du premier pour estimer le consentement marginal à payer des agents pour différentes caractéristiques du logement et du quartier à Paris. Il introduit une nouvelle procédure d'estimation basée sur le modèle de pures caractéristiques. Grâce à un riche jeu de données sur les achats de logements à Paris, nous montrons que le revenu moyen du voisinage et le niveau de criminalité sont de puissants déterminants du choix du quartier pour tous les types d'acheteurs, que l'accessibilité à l'emploi est également un facteur déterminant pour les ménages comptant plus d'une personne, et que la qualité de l'école du secteur joue un rôle primordial pour les ménages avec enfants. Le troisième chapitre, écrit conjointement avec Guillaume Chapelle, Alain Trannoy et Etienne Wasmer, montre que la croissance récente du ratio patrimoine sur revenu est due uniquement à l'augmentation du prix des logements, et plus précisément à l'augmentation du prix d'un facteur fixe de production: la terre. Nous montrons ensuite qu'un système de taxation du patrimoine doit taxer le facteur fixe qu'est la terre à des fins de redistribution et non le capital productif pour ne pas décourager l'investissement. / The first two of the three chapters of this thesis examine the identification and the estimation of discrete choice models. The first chapter proves the equivalence between matching models and discrete choice models, and draws the consequences in terms of identification and estimation. The second chapter builds on the results of the first, and uses matching algorithms to estimate the marginal willingness to pay of households for various housing and neighborhood characteristics in Paris (such as school performance, crime level, distance to employment areas). The third chapter deals with another topic: it first shows that the recent rise in the capital-income ratio highlighted by Thomas Piketty in his book is due to the rise in housing prices, and it then explores the consequences in terms of wealth distribution.

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A Violência entre Parceiros Íntimos (VPI) tem sido reconhecida como um importante problema de saúde pública e um fator de risco para agravos a saúde de mulheres e crianças. Os serviços de saúde desempenham importante papel na detecção precoce da VPI, especialmente em momentos da vida nos quais se preconiza o atendimento sistematizado, como na gestação e primeira infância. Esta dissertação tem como objetivo principal estimar a probabilidade de ocorrência de Violência Física entre Parceiros Íntimos (VFPI) durante a gestação e/ou pós-parto em população atendida em Unidades Básicas de Saúde (UBS), segundo diferentes características sócio-econômicas e demográficas da clientela. Trata-se de um estudo transversal, realizado com usuárias de 5 UBS da cidade do Rio de Janeiro no ano de 2007. Foram entrevistadas 811 mães de crianças de até cinco meses de idade, que não possuíam nenhuma contra-indicação formal para a amamentação e que relataram ter tido pelo menos uma relação amorosa um mês ou mais durante a gestação ou no período do pós-parto. Condições socioeconômicas e demográficas e relativas aos hábitos de vida do casal foram consideradas como potenciais preditores de violência. Utilizou-se a versão em português da CTS2 para identificar as situações de VPI. A variável de desfecho foi analisada em três níveis: ausência de VFPI, presença de VFPI no período da gestação ou do pós-parto e presença de VFPI em ambos os períodos. Utilizou-se um modelo logito-multinomial para as projeções de prevalências segundo os descritores selecionados. Os fatores que mais aumentaram a probabilidade de ocorrência de violência durante a gestação e/ou nos primeiros cinco meses de vida da criança foram: idade materna < 20 anos, escolaridade materna inferior ao 2 grau completo, ter 2 ou mais filhos menores de cinco anos, tabagismo materno, uso inadequado de álcool pela mãe e/ou companheiro, uso de drogas pela mãe e/ou companheiro e percepção materna sobre a saúde do bebê aquém da esperada. Entre mães com todas estas características, a estimativa de prevalência projetada de VFPI na gestação e/ou no pós-parto chegou a 96,4%, sendo 59,4% a estimativa de ocorrência em apenas um dos dois períodos e 37% em ambos. Por outro lado, a probabilidade de ocorrência de VFPI cai a 3,6% em famílias sem estas características. Os resultados indicam que a presença de certas características da criança e de sua família aumenta enormemente a probabilidade de ocorrência de VFPI, devendo ser levadas em consideração ao se estabelecer estratégias de intervenção que visem à detecção precoce e uma efetiva intervenção. / Intimate partner violence (IPV) has been recognized as an important public health problem and a risk factor for health problems of women and children. Health services play an important role in early detection of IPV. This issue is especially important in moments of life when systematized care is recommended, such as the pregnancy and early childhood. The main objective of this research was to estimate the probability of physical intimate partners violence (PIPV) during pregnancy or postpartum period. This is a cross-sectional study carried out in 5 primary health care units in Rio de Janeiro during the year 2007. Eight hundred and eleven interviews with mothers of children up to five months of age were carried out. Mothers presenting any formal contraindication for breastfeeding were considered ineligible, as well as women not reporting at least one month of amorous relationship during the pregnancy or postpartum period. Socioeconomic, demographic and life habits of the couple were considered as potential predictors. The outcome variable was assessed at three levels: no PIPV; PIPV during the pregnancy or postpartum; and PIPV in both periods. A multinomial logit model was used for projecting the respective prevalence according to a range of selected descriptors. The risk factors significantly associated with a greater risk of PIPV were: maternal age < 20; women with less than twelve years of schooling; women with 2 or more children under five years old; alcohol misuse by mother or partner; illicit drug abuse by the women or partner; and mothers perception of infants health lower than expected. Between mothers with all those characteristics, the projected prevalence of PIPV during pregnancy and/or postpartum was 96.4%, and as much as 59.4% accounted for the occurrence in one of the periods and 37% for the occurrence in both periods. In the absence of all of those factors, estimates reached only 3.6% during pregnancy and/or postpartum Summarizing, this study disclosed that some characteristics of children and their family increases the probability of PIPV during the pregnancy and postpartum period. This information is valuable for achieving early identification and effective resolution of the problem.

A Violência entre Parceiros Íntimos (VPI) tem sido reconhecida como um importante problema de saúde pública e um fator de risco para agravos a saúde de mulheres e crianças. Os serviços de saúde desempenham importante papel na detecção precoce da VPI, especialmente em momentos da vida nos quais se preconiza o atendimento sistematizado, como na gestação e primeira infância. Esta dissertação tem como objetivo principal estimar a probabilidade de ocorrência de Violência Física entre Parceiros Íntimos (VFPI) durante a gestação e/ou pós-parto em população atendida em Unidades Básicas de Saúde (UBS), segundo diferentes características sócio-econômicas e demográficas da clientela. Trata-se de um estudo transversal, realizado com usuárias de 5 UBS da cidade do Rio de Janeiro no ano de 2007. Foram entrevistadas 811 mães de crianças de até cinco meses de idade, que não possuíam nenhuma contra-indicação formal para a amamentação e que relataram ter tido pelo menos uma relação amorosa um mês ou mais durante a gestação ou no período do pós-parto. Condições socioeconômicas e demográficas e relativas aos hábitos de vida do casal foram consideradas como potenciais preditores de violência. Utilizou-se a versão em português da CTS2 para identificar as situações de VPI. A variável de desfecho foi analisada em três níveis: ausência de VFPI, presença de VFPI no período da gestação ou do pós-parto e presença de VFPI em ambos os períodos. Utilizou-se um modelo logito-multinomial para as projeções de prevalências segundo os descritores selecionados. Os fatores que mais aumentaram a probabilidade de ocorrência de violência durante a gestação e/ou nos primeiros cinco meses de vida da criança foram: idade materna < 20 anos, escolaridade materna inferior ao 2 grau completo, ter 2 ou mais filhos menores de cinco anos, tabagismo materno, uso inadequado de álcool pela mãe e/ou companheiro, uso de drogas pela mãe e/ou companheiro e percepção materna sobre a saúde do bebê aquém da esperada. Entre mães com todas estas características, a estimativa de prevalência projetada de VFPI na gestação e/ou no pós-parto chegou a 96,4%, sendo 59,4% a estimativa de ocorrência em apenas um dos dois períodos e 37% em ambos. Por outro lado, a probabilidade de ocorrência de VFPI cai a 3,6% em famílias sem estas características. Os resultados indicam que a presença de certas características da criança e de sua família aumenta enormemente a probabilidade de ocorrência de VFPI, devendo ser levadas em consideração ao se estabelecer estratégias de intervenção que visem à detecção precoce e uma efetiva intervenção. / Intimate partner violence (IPV) has been recognized as an important public health problem and a risk factor for health problems of women and children. Health services play an important role in early detection of IPV. This issue is especially important in moments of life when systematized care is recommended, such as the pregnancy and early childhood. The main objective of this research was to estimate the probability of physical intimate partners violence (PIPV) during pregnancy or postpartum period. This is a cross-sectional study carried out in 5 primary health care units in Rio de Janeiro during the year 2007. Eight hundred and eleven interviews with mothers of children up to five months of age were carried out. Mothers presenting any formal contraindication for breastfeeding were considered ineligible, as well as women not reporting at least one month of amorous relationship during the pregnancy or postpartum period. Socioeconomic, demographic and life habits of the couple were considered as potential predictors. The outcome variable was assessed at three levels: no PIPV; PIPV during the pregnancy or postpartum; and PIPV in both periods. A multinomial logit model was used for projecting the respective prevalence according to a range of selected descriptors. The risk factors significantly associated with a greater risk of PIPV were: maternal age < 20; women with less than twelve years of schooling; women with 2 or more children under five years old; alcohol misuse by mother or partner; illicit drug abuse by the women or partner; and mothers perception of infants health lower than expected. Between mothers with all those characteristics, the projected prevalence of PIPV during pregnancy and/or postpartum was 96.4%, and as much as 59.4% accounted for the occurrence in one of the periods and 37% for the occurrence in both periods. In the absence of all of those factors, estimates reached only 3.6% during pregnancy and/or postpartum Summarizing, this study disclosed that some characteristics of children and their family increases the probability of PIPV during the pregnancy and postpartum period. This information is valuable for achieving early identification and effective resolution of the problem.

This project deals vith analysis and testing of algorithms and statistical models, that could potentionaly improve resuts of FIT BUT in ImageNet Large Scale Visual Recognition Challenge and TRECVID. Multinomial model was tested. Phonotactic Intersession Variation Compensation (PIVCO) model was used for reducing random e ffects in image representation and for dimensionality reduction. PIVCO - dimensionality reduction achieved the best mean average precision while reducing to one-twenyth of original dimension. KPCA model was tested to approximate Kernel SVM. All statistical models were tested on Pascal VOC 2007 dataset.

The aim of this work is to create a web application for automatic topic detection and segmentation of on-line courses. During playback of processed records, the application should be able to offer records from thematically consistent on-line courses. This document contains problem description, list of used instruments, description of implementation, the principle of operation and description of final user interface.

In a single capture-recapture problem, two new Wilson methods for interval estimation of population size are derived. Classical Chapman interval, Wilson and Wilson-cc intervals are examined and compared in terms of their expected interval width and exact coverage properties in two models. The new approach performs better than the Chapman in each model. Bayesian analysis also gives a different way to estimate population size.