On Option Price Information Content and Extraction of Implied Probability Distributions

In this study we used market settlement prices of European call options on stock index futures to extract implied probability distribution function (PDF). The method used produces a PDF of returns of an underlying asset at expiration date from implied volatility smile. With this method, the assumption of lognormal distribution (Black-Scholes model) is tested. The market view of the asset price dynamics can then be used for various purposes (hedging, speculation). We used the so called smoothing approach for implied PDF extraction presented by Shimko (1993). In our analysis we obtained implied volatility smiles from index futures markets (S&P 500 and DAX indices) and standardized them. The method introduced by Breeden and Litzenberger (1978) was then used on PDF extraction. The results show significant deviations from the assumption of lognormal returns for S&P500 options while DAX options mostly fit the lognormal distribution. A deviant subjective view of PDF can be used to form a strategy as discussed in the last section.

Assessing the use of very high resolution data to predict species distribution in a mountain environment

Nowadays, Species Distribution Models (SDMs) are a widely used tool. Using different statistical approaches these models reconstruct the realized niche of a species using presence data and a set of variables, often topoclimatic. There utilization range is quite large from understanding single species requirements, to the creation of nature reserve based on species hotspots, or modeling of climate change impact, etc... Most of the time these models are using variables at a resolution of 50km x 50km or 1 km x 1 km. However in some cases these models are used with resolutions below the kilometer scale and thus called high resolution models (100 m x 100 m or 25 m x 25 m). Quite recently a new kind of data has emerged enabling precision up to lm x lm and thus allowing very high resolution modeling. However these new variables are very costly and need an important amount of time to be processed. This is especially the case when these variables are used in complex calculation like models projections over large areas. Moreover the importance of very high resolution data in SDMs has not been assessed yet and is not well understood. Some basic knowledge on what drive species presence-absences is still missing. Indeed, it is not clear whether in mountain areas like the Alps coarse topoclimatic gradients are driving species distributions or if fine scale temperature or topography are more important or if their importance can be neglected when balance to competition or stochasticity. In this thesis I investigated the importance of very high resolution data (2-5m) in species distribution models using either very high resolution topographic, climatic or edaphic variables over a 2000m elevation gradient in the Western Swiss Alps. I also investigated more local responses of these variables for a subset of species living in this area at two precise elvation belts. During this thesis I showed that high resolution data necessitates very good datasets (species and variables for the models) to produce satisfactory results. Indeed, in mountain areas, temperature is the most important factor driving species distribution and needs to be modeled at very fine resolution instead of being interpolated over large surface to produce satisfactory results. Despite the instinctive idea that topographic should be very important at high resolution, results are mitigated. However looking at the importance of variables over a large gradient buffers the importance of the variables. Indeed topographic factors have been shown to be highly important at the subalpine level but their importance decrease at lower elevations. Wether at the mountane level edaphic and land use factors are more important high resolution topographic data is more imporatant at the subalpine level. Finally the biggest improvement in the models happens when edaphic variables are added. Indeed, adding soil variables is of high importance and variables like pH are overpassing the usual topographic variables in SDMs in term of importance in the models. To conclude high resolution is very important in modeling but necessitate very good datasets. Only increasing the resolution of the usual topoclimatic predictors is not sufficient and the use of edaphic predictors has been highlighted as fundamental to produce significantly better models. This is of primary importance, especially if these models are used to reconstruct communities or as basis for biodiversity assessments. -- Ces dernières années, l'utilisation des modèles de distribution d'espèces (SDMs) a continuellement augmenté. Ces modèles utilisent différents outils statistiques afin de reconstruire la niche réalisée d'une espèce à l'aide de variables, notamment climatiques ou topographiques, et de données de présence récoltées sur le terrain. Leur utilisation couvre de nombreux domaines allant de l'étude de l'écologie d'une espèce à la reconstruction de communautés ou à l'impact du réchauffement climatique. La plupart du temps, ces modèles utilisent des occur-rences issues des bases de données mondiales à une résolution plutôt large (1 km ou même 50 km). Certaines bases de données permettent cependant de travailler à haute résolution, par conséquent de descendre en dessous de l'échelle du kilomètre et de travailler avec des résolutions de 100 m x 100 m ou de 25 m x 25 m. Récemment, une nouvelle génération de données à très haute résolution est apparue et permet de travailler à l'échelle du mètre. Les variables qui peuvent être générées sur la base de ces nouvelles données sont cependant très coûteuses et nécessitent un temps conséquent quant à leur traitement. En effet, tout calcul statistique complexe, comme des projections de distribution d'espèces sur de larges surfaces, demande des calculateurs puissants et beaucoup de temps. De plus, les facteurs régissant la distribution des espèces à fine échelle sont encore mal connus et l'importance de variables à haute résolution comme la microtopographie ou la température dans les modèles n'est pas certaine. D'autres facteurs comme la compétition ou la stochasticité naturelle pourraient avoir une influence toute aussi forte. C'est dans ce contexte que se situe mon travail de thèse. J'ai cherché à comprendre l'importance de la haute résolution dans les modèles de distribution d'espèces, que ce soit pour la température, la microtopographie ou les variables édaphiques le long d'un important gradient d'altitude dans les Préalpes vaudoises. J'ai également cherché à comprendre l'impact local de certaines variables potentiellement négligées en raison d'effets confondants le long du gradient altitudinal. Durant cette thèse, j'ai pu monter que les variables à haute résolution, qu'elles soient liées à la température ou à la microtopographie, ne permettent qu'une amélioration substantielle des modèles. Afin de distinguer une amélioration conséquente, il est nécessaire de travailler avec des jeux de données plus importants, tant au niveau des espèces que des variables utilisées. Par exemple, les couches climatiques habituellement interpolées doivent être remplacées par des couches de température modélisées à haute résolution sur la base de données de terrain. Le fait de travailler le long d'un gradient de température de 2000m rend naturellement la température très importante au niveau des modèles. L'importance de la microtopographie est négligeable par rapport à la topographie à une résolution de 25m. Cependant, lorsque l'on regarde à une échelle plus locale, la haute résolution est une variable extrêmement importante dans le milieu subalpin. À l'étage montagnard par contre, les variables liées aux sols et à l'utilisation du sol sont très importantes. Finalement, les modèles de distribution d'espèces ont été particulièrement améliorés par l'addition de variables édaphiques, principalement le pH, dont l'importance supplante ou égale les variables topographique lors de leur ajout aux modèles de distribution d'espèces habituels.

Use of Statistical Methods in Demand Planning

In a very volatile industry of high technology it is of utmost importance to accurately forecast customers’ demand. However, statistical forecasting of sales, especially in heavily competitive electronics product business, has always been a challenging task due to very high variation in demand and very short product life cycles of products. The purpose of this thesis is to validate if statistical methods can be applied to forecasting sales of short life cycle electronics products and provide a feasible framework for implementing statistical forecasting in the environment of the case company. Two different approaches have been developed for forecasting on short and medium term and long term horizons. Both models are based on decomposition models, but differ in interpretation of the model residuals. For long term horizons residuals are assumed to represent white noise, whereas for short and medium term forecasting horizon residuals are modeled using statistical forecasting methods. Implementation of both approaches is performed in Matlab. Modeling results have shown that different markets exhibit different demand patterns and therefore different analytical approaches are appropriate for modeling demand in these markets. Moreover, the outcomes of modeling imply that statistical forecasting can not be handled separately from judgmental forecasting, but should be perceived only as a basis for judgmental forecasting activities. Based on modeling results recommendations for further deployment of statistical methods in sales forecasting of the case company are developed.

The effect of skewness and kurtosis on the Kenward-Roger approximation when group distributions differ

This study examined the independent effect of skewness and kurtosis on the robustness of the linear mixed model (LMM), with the Kenward-Roger (KR) procedure, when group distributions are different, sample sizes are small, and sphericity cannot be assumed. Methods: A Monte Carlo simulation study considering a split-plot design involving three groups and four repeated measures was performed. Results: The results showed that when group distributions are different, the effect of skewness on KR robustness is greater than that of kurtosis for the corresponding values. Furthermore, the pairings of skewness and kurtosis with group size were found to be relevant variables when applying this procedure. Conclusions: With sample sizes of 45 and 60, KR is a suitable option for analyzing data when the distributions are: (a) mesokurtic and not highly or extremely skewed, and (b) symmetric with different degrees of kurtosis. With total sample sizes of 30, it is adequate when group sizes are equal and the distributions are: (a) mesokurtic and slightly or moderately skewed, and sphericity is assumed; and (b) symmetric with a moderate or high/extreme violation of kurtosis. Alternative analyses should be considered when the distributions are highly or extremely skewed and samples sizes are small.

Statistical hypothesis testing and common misinterpretations: should we abandon p-value in forensic science applications?

Many people regard the concept of hypothesis testing as fundamental to inferential statistics. Various schools of thought, in particular frequentist and Bayesian, have promoted radically different solutions for taking a decision about the plausibility of competing hypotheses. Comprehensive philosophical comparisons about their advantages and drawbacks are widely available and continue to span over large debates in the literature. More recently, controversial discussion was initiated by an editorial decision of a scientific journal [1] to refuse any paper submitted for publication containing null hypothesis testing procedures. Since the large majority of papers published in forensic journals propose the evaluation of statistical evidence based on the so called p-values, it is of interest to expose the discussion of this journal's decision within the forensic science community. This paper aims to provide forensic science researchers with a primer on the main concepts and their implications for making informed methodological choices.

Statistics in Public Understanding of Science review: How to achieve high statistical standards?

This article proposes a checklist to improve statistical reporting in the manuscripts submitted to Public Understanding of Science. Generally, these guidelines will allow the reviewers (and readers) to judge whether the evidence provided in the manuscript is relevant. The article ends with other suggestions for a better statistical quality of the journal.

On the physical realizability of highly focused electromagnetic field distributions

A method to evaluate the physical realizability of an arbitrary three-dimensional vectorial field distribution in the focal area is proposed. A parameter that measures the similarity between the designed (target) field and the physically achievable beam is provided. This analysis is carried out within the framework of the closest electromagnetic field to a given vectorial function, and the procedure is applied to two illustrative cases.

Regional heterogeneity in wage distributions. Evidence from Spain.

Regional differences in real wages have been shown to be both large and persistent in the U.S. and the U.K., as well as in the economies of other countries. Empirical evidence suggests that wage differentials adjusted for the cost of living cannot only be explained by the unequal spatial distribution of characteristics determining earnings. Rather, average wage gap decomposition reveals the important contribution made by regional heterogeneity in the price assigned to these characteristics. This paper proposes a method for assessing regional disparities in the entire wage distribution and for decomposing the effect of differences across regions in the endowments and prices of the characteristics. The hypothesis forwarded is that the results from previous studies obtained by comparing average regional wages may be partial and nonrobust. Empirical evidence from a matched employer-employee dataset for Spain confirms marked differences in wage distributions between regions, which do not result from worker and firm characteristics but from the increasing role of regional differences in the return to human capital.

Statistical Methods for Conservation and Alignment Quality in Proteins

Construction of multiple sequence alignments is a fundamental task in Bioinformatics. Multiple sequence alignments are used as a prerequisite in many Bioinformatics methods, and subsequently the quality of such methods can be critically dependent on the quality of the alignment. However, automatic construction of a multiple sequence alignment for a set of remotely related sequences does not always provide biologically relevant alignments.Therefore, there is a need for an objective approach for evaluating the quality of automatically aligned sequences. The profile hidden Markov model is a powerful approach in comparative genomics. In the profile hidden Markov model, the symbol probabilities are estimated at each conserved alignment position. This can increase the dimension of parameter space and cause an overfitting problem. These two research problems are both related to conservation. We have developed statistical measures for quantifying the conservation of multiple sequence alignments. Two types of methods are considered, those identifying conserved residues in an alignment position, and those calculating positional conservation scores. The positional conservation score was exploited in a statistical prediction model for assessing the quality of multiple sequence alignments. The residue conservation score was used as part of the emission probability estimation method proposed for profile hidden Markov models. The results of the predicted alignment quality score highly correlated with the correct alignment quality scores, indicating that our method is reliable for assessing the quality of any multiple sequence alignment. The comparison of the emission probability estimation method with the maximum likelihood method showed that the number of estimated parameters in the model was dramatically decreased, while the same level of accuracy was maintained. To conclude, we have shown that conservation can be successfully used in the statistical model for alignment quality assessment and in the estimation of emission probabilities in the profile hidden Markov models.

Statistical Analysis of an SEIR Epidemic Model

This thesis was focussed on statistical analysis methods and proposes the use of Bayesian inference to extract information contained in experimental data by estimating Ebola model parameters. The model is a system of differential equations expressing the behavior and dynamics of Ebola. Two sets of data (onset and death data) were both used to estimate parameters, which has not been done by previous researchers in (Chowell, 2004). To be able to use both data, a new version of the model has been built. Model parameters have been estimated and then used to calculate the basic reproduction number and to study the disease-free equilibrium. Estimates of the parameters were useful to determine how well the model fits the data and how good estimates were, in terms of the information they provided about the possible relationship between variables. The solution showed that Ebola model fits the observed onset data at 98.95% and the observed death data at 93.6%. Since Bayesian inference can not be performed analytically, the Markov chain Monte Carlo approach has been used to generate samples from the posterior distribution over parameters. Samples have been used to check the accuracy of the model and other characteristics of the target posteriors.

Statistical Optimum Design of Heat Exchangers

The optimal design of a heat exchanger system is based on given model parameters together with given standard ranges for machine design variables. The goals set for minimizing the Life Cycle Cost (LCC) function which represents the price of the saved energy, for maximizing the momentary heat recovery output with given constraints satisfied and taking into account the uncertainty in the models were successfully done. Nondominated Sorting Genetic Algorithm II (NSGA-II) for the design optimization of a system is presented and implemented inMatlab environment. Markov ChainMonte Carlo (MCMC) methods are also used to take into account the uncertainty in themodels. Results show that the price of saved energy can be optimized. A wet heat exchanger is found to be more efficient and beneficial than a dry heat exchanger even though its construction is expensive (160 EUR/m2) compared to the construction of a dry heat exchanger (50 EUR/m2). It has been found that the longer lifetime weights higher CAPEX and lower OPEX and vice versa, and the effect of the uncertainty in the models has been identified in a simplified case of minimizing the area of a dry heat exchanger.

Validation and statistical analysis of two high performance liquid chromatography methods for the determination of indinavir sulfate raw material and capsules

Two high performance liquid chromatography (HPLC) methods for the quantitative determination of indinavir sulfate were tested, validated and statistically compared. Assays were carried out using as mobile phases mixtures of dibutylammonium phosphate buffer pH 6.5 and acetonitrile (55:45) at 1 mL/min or citrate buffer pH 5 and acetonitrile (60:40) at 1 mL/min, an octylsilane column (RP-8) and a UV spectrophotometric detector at 260 nm. Both methods showed good sensitivity, linearity, precision and accuracy. The statistical analysis using the t-student test for the determination of indinavir sulfate raw material and capsules indicated no statistically significant difference between the two methods.