Essays on Financial Returns' Distributions Modelling with Applications

This thesis consists of three main chapters. Its first and second chapters are concerned with univariate distributions modelling of financial data, while the third chapter has more applied and pragmatic financial scope of the Value-at-Risk estimations. First chapter targets developing new parametric distribution models for financial applications and suggests six of such models on the basis of Student's t distribution. Second chapter shifts to the field of nonparametric statistics for financial data in the time series estimations context and is concerned with selection of parameters for estimation of densities and distributions of financial returns with dynamic kernel methods. It compares performances of the dynamic kernel estimators under the parameters chosen by maximum likelihood and several least-squares routines. Third chapter, enriched with results from the previous substantive part, aims to position performance of the dynamic kernel estimator for distributions of financial returns within relevant group of methods for Value-at-Risk modelling and forecasting. Main chapters of this thesis are preceded by the preface section to summarize main motivations behind, provide overarching theme of the thesis, encompass some of its limitations and future research paths, which may follow from the conducted work, while main contributions of each chapter are also covered in the section concluding this work.