This paper describes methods for pricing European and American options. Monte Carlo simulation and control variates methods are employed to price call options. The binomial model is employed to price American put options. Using daily stock data I am able to compare the model price and market price and speculate as to the cause of difference. Lastly, I build a portfolio in an Interactive Brokers paper trading [1] account using the prices I calculate. This project was done a part of the masters capstone course Math 573: Computational Methods of Financial Mathematics.

<p>Syftet med uppsatsen är att försöka förklara vad det är som påverkar tiden som en mamma ammar. För att undersöka vad det är som påverkar tiden som en mamma ammar, har en Zero inflated negative binomial-modell (ZINB-modell) tagits fram. Resultaten visar att det som avgör hur länge en mamma kommer att amma är: Graviditetens längd, mammans ålder, mammans rökvanor under graviditetens sista månader, mammans rökvanor samt mammans nationella ursprung.</p>

Syftet med uppsatsen är att försöka förklara vad det är som påverkar tiden som en mamma ammar. För att undersöka vad det är som påverkar tiden som en mamma ammar, har en Zero inflated negative binomial-modell (ZINB-modell) tagits fram. Resultaten visar att det som avgör hur länge en mamma kommer att amma är: Graviditetens längd, mammans ålder, mammans rökvanor under graviditetens sista månader, mammans rökvanor samt mammans nationella ursprung.

This research assesses the performance of over-dispersed Poisson regression model and negative binomial model with count data. It examines the association between price plan features of mobile phone services and the number of people who adopt the plan. Mobile service data is used to estimate the model with a sample of one million customers running from February 2006 to September 2009. Under three main categories, customer type, age, and handset price, we run the model based on price plan features. Estimates are derived from the maximum likelihood estimation (MLE) method. Root mean squared error (RMSE) is used to observe the statistical fits of all the regression models. Then, we construct four estimation and holdout samples, leaving out one, three, six, and twelve months. The estimation constitutes the in-sample (IS) and the holdout represents the out-sample (OS). By estimating the IS, we predict the OS. Root mean squared error of prediction (RMSEP) is checked to see how accurate the prediction is. Results generally suggest that academic year start (AYS), seasonality, duration of months since launch of price plan (DMLP), basic fees, rate with no discount (RND), free call minutes (FCM), free data (FD), free text messaging (FTM), free perk rating (FPR), and handset support all show significant effect. The significance occurs depending on the segment. The RMSE and RMSEP show that the over-dispersed Poisson model outperforms the negative binomial model. Further implications and limitations of the results are discussed. / text

As one of the major data analysis methods, statistical models play an important role in traffic safety analysis. A common situation associated with crash data is the phenomenon known as overdispersion which has been discussed and investigated frequently in recent years. As such, researchers have proposed several models, such as the Poisson Gamma (PG) or Negative Binomial (NB), the Poisson-lognormal, or the Poisson-Weibull, to handle the overdispersion. Unfortunately, very few models have been proposed for specifically analyzing the sources of dispersions in the data. Better understanding of sources of variation and overdispersion could help in managing safety, such as establishing relationships and applying appropriate treatments or countermeasures, more efficiently. Given the limitations of existing models for exploring the source of overdispersion of crash data, this research examined a new model function that could be applied to explore sources of extra variability through the use of the Generalized Waring (GW) models. This model, which was recently introduced by statisticians, divides the observed variability into three components: randomness, internal differences between road segments or intersections, and the variances caused by other external factors that have not been included as covariates in the model. To evaluate these models, GW models were examined using both simulated and empirical crash datasets, and the results were compared to the most commonly used NB model and the recently developed NB-Lindley models. For model parameter estimation, both the maximum likelihood method and a Bayesian approach were adopted for better comparison. A simulation study was used to show the better performance of this model compared to NB model for overdispersed data, and then an application in the empirical crash data illustrates its capability of modeling data sets with great accuracy and exploring the source of overdispersion. The performances of hotspot identification for these two kinds of models (i.e., GW models and NB models) were also examined and compared based on the estimated models from the empirical dataset. Finally, bias properties related to the choice of prior distributions for parameters in GW model were examined by using a simulation study. In addition, the suggestions on the choice of minimum sample size and priors were presented for different kinds of datasets.

The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of zero-inflated and hurdle regression models in the functions zeroinfl() and hurdle() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both model classes are able to incorporate over-dispersion and excess zeros - two problems that typically occur in count data sets in economics and the social and political sciences - better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of hurdle and zero-inflated regression models in the functions hurdle() and zeroinfl() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both hurdle and zero-inflated model, are able to incorporate over-dispersion and excess zeros-two problems that typically occur in count data sets in economics and the social sciences-better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice. (authors' abstract)

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

Metagenomics is the study of a collective microbial genetic content recovered directly from natural (e.g., soil, ocean, and freshwater) or host-associated (e.g., human gut, skin, and oral) environmental communities that contain microorganisms, i.e., microbiomes. The rapid technological developments in next generation sequencing (NGS) technologies, enabling to sequence tens or hundreds of millions of short DNA fragments (or reads) in a single run, facilitates the studies of multiple microorganisms lived in environmental communities. Metagenomics, a relatively new but fast growing field, allows us to understand the diversity of microbes, their functions, cooperation, and evolution in a particular ecosystem. Also, it assists us to identify significantly different metabolic potentials in different environments. Particularly, metagenomic analysis on the basis of functional features (e.g., pathways, subsystems, functional roles) enables to contribute the genomic contents of microbes to human health and leads us to understand how the microbes affect human health by analyzing a metagenomic data corresponding to two or multiple populations with different clinical phenotypes (e.g., diseased and healthy, or different treatments). Currently, metagenomic analysis has substantial impact not only on genetic and environmental areas, but also on clinical applications. In our study, we focus on the development of computational and statistical methods for functional metagnomic analysis of sequencing data that is obtained from various environmental microbial samples/communities.

The aim of this study is to examine the effects of a market-based greenhouse gases price on green innovation by testing the Hicksian theory of induced innovation. To test whether causality exists, panel data compiled of 30 countries over 13 years (2005-2017) have been used. The study is restricted to the European Union emission trading scheme, where the price of EUA has been used as a market-based price for greenhouse gases. To capture the effect on innovation, an approximation for innovation in the form of patent counts have been employed using the patent category Y02 constructed by the EPO. The result suggests that green innovation is affected by the price of the EUA, total CO2 emissions and tax revenue from energy. This study employed a knowledge stock variable that was not found to be significant, contrary to previous literature on induced innovation. The incidence rate ratio associated with the  permits price indicates that a one euro increase in price would result in a 1.135 % increase in the patenting of green technology. The result suggests that a higher price in  permits would stimulate innovation of green technology within the European Union.