This thesis studies binomial and trinomial lattice approximations in Black-Scholes type option pricing models. Also, it covers the basics of these models, derivations of model parameters by several methods under different kinds of distributions. Furthermore, the convergence of binomial model to normal distribution, Geometric Brownian Motion and Black-Scholes model isdiscussed. Finally, the connections and interrelations between discrete random variables under the Lattice approach and continuous random variables under models which follow Geometric Brownian Motion are discussed, compared and contrasted.

This thesis studies binomial and trinomial lattice approximations in Black-Scholes type option pricing models. Also, it covers the basics of these models, derivations of model parameters by several methods under different kinds of distributions. Furthermore, the convergence of the binomial model to normal distribution, Geometric Brownian Motion and Black-Scholes model is discussed. Finally, the connections and interrelations between discrete random variables under the Lattice approach and continuous random variables under models which follow Geometric Brownian Motion are discussed, compared and contrasted.

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We consider weak convergence of a sequence of asset price models (Sn) to a limiting asset price model S. A typical case for this situation is the convergence of a sequence of binomial models to the Black-Scholes model, as studied by Cox, Ross, and Rubinstein. We put emphasis on two different aspects of this convergence: firstly we consider convergence with respect to the given "physical" probability measures (Pn) and secondly with respect to the "risk-neutral" measures (Qn) for the asset price processes (Sn). (In the case of non-uniqueness of the risk-neutral measures also the question of the "good choice" of (Qn) arises.) In particular we investigate under which conditions the weak convergence of (Pn) to P implies the weak convergence of (Qn) to Q and thus the convergence of prices of derivative securities. The main theorem of the present paper exhibits an intimate relation of this question with contiguity properties of the sequences of measures (Pn) with respect to (Qn) which in turn is closely connected to asymptotic arbitrage properties of the sequence (Sn) of security price processes. We illustrate these results with general homogeneous binomial and some special trinomial models. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

This thesis investigates the relationship between conflict, economic growth, state capacity and natural resources in Sub-Saharan Africa. It contributes to the limited research in this area and empirically examines these relationships using different econometric models. The first empirical chapter uses a panel dataset that covers the period 1997 - 2013 to analyse the effects of economic growth on conflict in Nigeria using the negative binomial model. The findings support the direct relationship between economic growth and conflict in Nigeria. Controlling for other factors, the results indicate that increase in growth rate - measured by annual growth rate of GDP per capita - decreases the expected number of conflicts. The study finds no evidence of a relationship between levels of wealth in a state and the incidence of conflicts. The analysis controls for factors such as spill-over effects from other states and year and state effects. Finally, to address potential concerns that economic growth could be a cause of conflict or that other unobserved factors could confound the relationship between economic growth and conflict, the chapter employs instrumental variable (IV) estimation using percentage change in rainfall as an instrument. The results with the IV estimation are similar to the results without IV in terms of both sign and significance, indicating that the negative effect of economic growth on conflicts is not due to reverse causality or omitted variables. For robustness checks, a Panel Autoregressive model (PVAR) is also employed. The second empirical chapter analyses the effect of conflict on state capacity in Sub-Saharan Africa. State capacity is measured in terms of fiscal and legal capacity. It also looks at the effects of internal and external conflicts on state capacity. The chapter adopts the Ordinary least squared (OLS) and the system generalised methods of moments (GMM) estimation methods to analyse the panel data consisting of 49 Sub-Saharan countries over the period 2000 - 2015. The results suggest that conflicts have a negative and significant effect on state capacity. However, when military expenditure is used as a proxy for state capacity it is found that conflict strengthens state capacity. The results are consistent with theoretical argument that internal conflicts polarise societies and make it more difficult for governments to reach a consensus in investing in state capacity, while external conflicts mobilise domestic population against a common enemy thereby helping in state capacity building. Finally, the third empirical chapter examines the effect of natural resources on conflict onset and duration using discrete choice models with a dataset covering the period 1980 -2016. The results on the duration analysis show that natural resources prolong duration of conflicts. However, it is found that not all natural resources prolong duration of conflicts. Oil production does not seem to affect duration, whereas oil reserves and gas production lengthens the duration. The findings from the onset analysis show that both production and reserves of natural resources increase the risk of conflict onset.

Motor vehicle crashes have increasingly become a serious concern for highway safety engineers and transportation agencies over the past few decades. This serious concern has led to a great deal of research activities. One of these activities is to develop safety analysis tools, specifically crash prediction models, for the purpose of reducing crashes and enhancing highway safety.Crash prediction models based on statistical or econometric modeling techniques are used for a variety of purposes; most commonly to estimate the expected crash frequencies from various roadway entities (highways, intersections, interstates, etc.) and also to identify geometric, environmental, and operations factors that are associated with crashes. A comprehensive review of prior literature indicates that many researchers have mainly focused on the development of aggregate crash prediction models based on single equation estimation techniques to identify the influences of geometric, environmental, and traffic variables on a single counted outcome. In some cases, however, more than one dependent variable might be of interest and hence several equations are formulated at the same time. Such a multiple equation structure may require simultaneous (or joint) estimation techniques under some situations.This dissertation research develops simultaneous estimation approaches to account for contemporaneous correlation and endogeneity problems in crash data. Specifically, seemingly unrelated negative binomial models and simultaneous equation models are developed to account for contemporaneous correlation between the disturbance terms across crash type models and to control for the endogenous relationship between the presence of left-turn lanes and angle crashes.Modeling crash types may provide certain advantages to gain insights as to 1) identification of high-risk sites with respect to specific types of crashes, which is not revealed through crash totals, and 2) the differences between conditions that lead to various crash types, but the disturbance terms across crash types might be contemporaneously correlated due to the unobserved common characteristics. Therefore, individual and simultaneous crash type models were estimated and the results of both models were compared. The results showed that a simultaneous estimation approach provides more efficient estimators relative to a single equation estimation technique.The presence of left-turn lanes has been treated as exogenous in crash prediction models, but in fact they are affecting each other. The bi-directional relationship between left-turn lanes and crashes results in endogeneity. This research investigated the endogenous relationship between left-turn lanes and crashes and developed simultaneous equation models to control for the endogeneity. The findings indicated that the presence of left-turn lanes is endogenously associated with crashes and the real effect of left-turn lanes on crashes can be obtained by controlling for endogeneity.

This study examined differences in sexual risk behaviors by gender and over time among 1281 patients (777 males and 504 females) from 12 community-based substance use disorder treatment programs throughout the United States participating in CTN-0032, a randomized control trial conducted within the National Drug Abuse Treatment Clinical Trials Network. Zero-inflated negative binomial and negative binomial models were used in the statistical analysis. Results indicated significant reductions in most types of sexual risk behaviors among substance users regardless of the intervention arms. There were also significant gender differences in sexual risk behaviors. Men (compared with women) reported more condomless sex acts with their non-primary partners (IRR = 1.80, 95 % CI 1.21–2.69) and condomless anal sex acts (IRR = 1.74, 95 % CI 1.11–2.72), but fewer condomless sex partners (IRR = 0.87, 95 % CI 0.77–0.99), condomless vaginal sex acts (IRR = 0.83, 95 % CI 0.69–1.00), and condomless sex acts within 2 h of using drugs or alcohol (IRR = 0.70, 95 % CI 0.53–0.90). Gender-specific intervention approaches are called for in substance use disorder treatment.

Traffic crashes have been identified as one of the main causes of death in the US, making road safety a high priority issue that needs urgent attention. Recognizing the fact that more and effective research has to be done in this area, this thesis aims mainly at developing different statistical models related to the road safety. The thesis includes three main sections: 1) overall crash frequency analysis using negative binomial models, 2) seemingly unrelated negative binomial (SUNB) models for different categories of crashes divided based on type of crash, or condition in which they occur, 3) safety models to determine the probability of crash occurrence, including a rainfall index that has been estimated using a logistic regression model. The study corridor is a 36.25 mile stretch of Interstate 4 in Central Florida. For the first two sections, crash cases from 1999 through 2002 were considered. Conventionally most of the crash frequency analysis model all crashes, instead of dividing them based on type of crash, peaking conditions, availability of light, severity, or pavement condition, etc. Also researchers traditionally used AADT to represent traffic volumes in their models. These two cases are examples of macroscopic crash frequency modeling. To investigate the microscopic models, and to identify the significant factors related to crash occurrence, a preliminary study (first analysis) explored the use of microscopic traffic volumes related to crash occurrence by comparing AADT/VMT with five to twenty minute volumes immediately preceding the crash. It was found that the volumes just before the time of crash occurrence proved to be a better predictor of crash frequency than AADT. The results also showed that road curvature, median type, number of lanes, pavement surface type and presence of on/off-ramps are among the significant factors that contribute to crash occurrence. In the second analysis various possible crash categories were prepared to exactly identify the factors related to them, using various roadway, geometric, and microscopic traffic variables. Five different categories are prepared based on a common platform, e.g. type of crash. They are: 1) Multiple and Single vehicle crashes, 2) Peak and Off-peak crashes, 3) Dry and Wet pavement crashes, 4) Daytime and Dark hour crashes, and 5) Property Damage Only (PDO) and Injury crashes. Each of the above mentioned models in each category are estimated separately. To account for the correlation between the disturbance terms arising from omitted variables between any two models in a category, seemingly unrelated negative binomial (SUNB) regression was used, and then the models in each category were estimated simultaneously. SUNB estimation proved to be advantageous for two categories: Category 1, and Category 4. Road curvature and presence of On-ramps/Off-ramps were found to be the important factors, which can be related to every crash category. AADT was also found to be significant in all the models except for the single vehicle crash model. Median type and pavement surface type were among the other important factors causing crashes. It can be stated that the group of factors found in the model considering all crashes is a superset of the factors that were found in individual crash categories. The third analysis dealt with the development of a logistic regression model to obtain the weather condition at a given time and location on I-4 in Central Florida so that this information can be used in traffic safety analyses, because of the lack of weather monitoring stations in the study area. To prove the worthiness of the weather information obtained form the analysis, the same weather information was used in a safety model developed by Abdel-Aty et al., 2004. It was also proved that the inclusion of weather information actually improved the safety model with better prediction accuracy.

Made available in DSpace on 2016-06-02T20:06:03Z (GMT). No. of bitstreams: 1 2510.pdf: 1878422 bytes, checksum: 882e21e70271b7a106e3a27a080da004 (MD5) Previous issue date: 2009-04-06 / This work has as central theme the Inflated Modified Power Series Distributions, where the objective is to study its main properties and the applicability in the bayesian context. This class of models includes the generalized Poisson, binomial and negative binomial distributions. These probability distributions are very helpful to models discrete data with inflated values. As particular case the - zero inflated Poisson models (ZIP) is studied, where the main purpose was to verify the effectiveness of it when compared to the Poisson distribution. The same methodology was considered for the negative binomial inflated distribution, but comparing it with the Poisson, negative binomial and ZIP distributions. The Bayes factor and full bayesian significance test were considered for selecting models. / Este trabalho tem como tema central a classe de distribuições série de potências inflacionadas, em que o intuito é estudar suas principais propriedades e a aplicabilidade no contexto bayesiano. Esta classe de modelos engloba as distribuições de Poisson, binomial e binomial negativa simples e as generalizadas e, por isso é muito aplicada na modelagem de dados discretos com valores excessivos. Como caso particular propôs-se explorar a distribuição de Poisson zero inflacionada (ZIP), em que o objetivo principal foi verificar a eficácia de sua modelagem quando comparada à distribuição de Poisson. A mesma metodologia foi considerada para a distribuição binomial negativa inflacionada, mas comparando-a com as distribuições de Poisson, binomial negativa e ZIP. Como critérios formais para seleção de modelos foram considerados o fator de Bayes e o teste de significância completamente bayesiano.