The diploma thesis deals with modelling of time series (stock and commodities) by using the models of volatility. The theoretical part focuses on the term of volatility and other terms connected to it. There is a theoretical description of the models as well. The practical part of the thesis focuses on the analysis of the time series and modelling of volatility using the program R.

This thesis investigates the application of the Black-Scholes model for pricing long-maturity options, primarily utilizing historical data on S\&P500 options. It compares prices computed with the Black-Scholes formula to actual market prices and critically examines the validity of the Black-Scholes model assumptions over long time frames. The assumptions mainly focused on are the constant volatility assumption, the assumption of normally distributed returns, the constant interest rate assumption and the no transaction cost assumption. The results show that the differences between computed prices and actual prices decrease as options get closer to maturity. They also show that several of the Black-Scholes model assumptions are not entirely realistic over long time frames. The conclusion of the thesis is that there are several limitations to the Black-Scholes model when it comes to pricing long-maturity options.

This thesis deals with the issue of subcontracting model of financial management and its impact on the economy of the construction enterprise. The aim of this work is to set up management of the building contract from the financial management of subcontracts with influence on the overall management of construction enterprise. The output of this work is a model that will point to the financial management of construction contracts regard to the management of construction enterprise.

Cette thèse est consacrée à l'étude des applications de la théorie des erreurs par formes de Dirichlet. Notre travail se divise en trois parties. La première analyse les modèles gouvernés par une équation différentielle stochastique. Après un court chapitre technique, un modèle innovant pour les carnets d’ordres est proposé. Nous considérons que le spread bid-ask n'est pas un défaut, mais plutôt une propriété intrinsèque du marché. L'incertitude est portée par le mouvement Brownien qui conduit l'actif. Nous montrons que l'évolution des spread peut être évaluée grâce à des formules fermées et nous étudions l'impact de l'incertitude du sous-jacent sur les produits dérivés. En suite, nous introduisons le modèle PBS pour le pricing des options européennes. L'idée novatrice est de distinguer la volatilité du marché par rapport au paramètre utilisé par les traders pour se couvrir. Nous assumons la première constante, alors que le deuxième devient une estimation subjective et erronée de la première. Nous prouvons que ce modèle prévoit un spread bid-ask et un smile de volatilité. Les propriétés plus intéressantes de ce modèle sont l’existence de formules fermés pour le pricing, l'impact de la dérive du sous-jacent et une efficace stratégie de calibration. La seconde partie s'intéresse aux modèles décrit par une équation aux dérivées partielles. Les cas linéaire et non-linéaire sont analysés séparément. Dans le premier nous montrons des relations intéressantes entre la théorie des erreurs et celui des ondelettes. Dans le cas non-linéaire nous étudions la sensibilité des solutions à l’aide de la théorie des erreurs. Sauf dans le cas d’une solution exacte, il y a deux approches possibles : on peut d’abord discrétiser l’EDP et étudier la sensibilité du problème discrétisé, soit démontrer que les sensibilités théoriques vérifient des EDP. Les deux cas sont étudiés, et nous prouvons que les sharp et le biais sont solutions d’EDP linéaires dépendantes de la solution de l’EDP originaire et nous proposons des algorithmes pour évaluer numériquement les sensibilités. Enfin, la troisième partie est dédiée aux équations stochastiques aux dérivées partielles. Notre analyse se divise en deux chapitres. D’abord nous étudions la transmission de l’incertitude, présente dans la condition initiale, à la solution de l’EDPS. En suite, nous analysons l'impact d'une perturbation dans les termes fonctionnelles de l’EDPS et dans le coefficient de la fonction de Green associée. Dans le deux cas, nous prouvons que le sharp et le biais sont solutions de deux EDPS linéaires dépendantes de la solution de l’EDPS originaire / This thesis is devoted to the study of the applications of the error theory using Dirichlet forms. Our work is split into three parts. The first one deals with the models described by stochastic differential equations. After a short technical chapter, an innovative model for order books is proposed. We assume that the bid-ask spread is not an imperfection, but an intrinsic property of exchange markets instead. The uncertainty is carried by the Brownian motion guiding the asset. We find that spread evolutions can be evaluated using closed formulae and we estimate the impact of the underlying uncertainty on the related contingent claims. Afterwards, we deal with the PBS model, a new model to price European options. The seminal idea is to distinguish the market volatility with respect to the parameter used by traders for hedging. We assume the former constant, while the latter volatility being an erroneous subjective estimation of the former. We prove that this model anticipates a bid-ask spread and a smiled implied volatility curve. Major properties of this model are the existence of closed formulae for prices, the impact of the underlying drift and an efficient calibration strategy. The second part deals with the models described by partial differential equations. Linear and non-linear PDEs are examined separately. In the first case, we show some interesting relations between the error and wavelets theories. When non-linear PDEs are concerned, we study the sensitivity of the solution using error theory. Except when exact solution exists, two possible approaches are detailed: first, we analyze the sensitivity obtained by taking “derivatives” of the discrete governing equations. Then, we study the PDEs solved by the sensitivity of the theoretical solutions. In both cases, we show that sharp and bias solve linear PDE depending on the solution of the former PDE itself and we suggest algorithms to evaluate numerically the sensitivities. Finally, the third part is devoted to stochastic partial differential equations. Our analysis is split into two chapters. First, we study the transmission of an uncertainty, present on starting conditions, on the solution of SPDE. Then, we analyze the impact of a perturbation of the functional terms of SPDE and the coefficient of the related Green function. In both cases, we show that the sharp and bias verify linear SPDE depending on the solution of the former SPDE itself / Questa tesi é dedicata allo studio delle applicazioni della teoria degli errori tramite forme di Dirichlet, il nostro lavoro si divide in tre parti. Nella prima vengono studiati i modelli descritti da un’equazione differenziale stocastica: dopo un breve capitolo con risultati tecnici viene descritto un modello innovativo per i libri d’ordini. La presenza dei differenziali denarolettera viene considerata non come un’imperfezione, bensi una proprietà intrinseca dei mercati. L’incertezza viene descritta come un rumore sul moto Browniano sottostante all’azione; dimostriamo che l’evoluzione di questi differenziali puó essere valutata attraverso formule chiuse e stimiamo l’impatto dell’incertezza del sottostante sui prodotti derivati. In seguito proponiamo un nuovo modello, chiamato PBS, per il prezzaggio delle opzioni di tipo europeo: l’idea innovativa consiste nel distinguere la volatilità di mercato dal parametro usato dai trader per la copertura. Noi supponiamo la prima constante, mentre il secondo diventa una stima soggettiva ed erronea della prima. Dimostriamo che questo modello prevede dei differenziali lettera-denaro e uno smile di volatilità implicita. Le maggiori proprietà di questo modello sono l’esistenza di formule chiuse per il princing, l’impatto del drift del sottostante e un’efficace strategia per la calibrazione. La seconda parte è dedicata allo studio dei modelli descritti da delle equazioni alle derivate perziali. I casi lineare e non-lineare sono trattati separatamente. Nel primo caso mostriamo interessanti relazioni tra la teoria degli errori e quella delle wavelets. Nel caso delle EDP non-lineari studiamo la sensibilità della soluzione usando la teoria degli errori. Due possibili approcci esistono, salvo quando la soluzione è esplicita. Possiamo prima discretizzare il problema e studiare la sensibilità delle equazioni discretizzate, oppure possiamo dimostrare che le sensibilità teoriche verificano, a loro volta, delle EDP dipendenti dalla soluzione della EDP iniziale. Entrambi gli approcci sono descritti e vengono proposti degli algoritmi per valutare le sensibilità numericamente. Infine, la terza parte è dedicata ai modelli descritti da un’equazione stocastica alle derivate parziali. La nostra analisi é divisa in due capitoli. Nel primo viene studiato l’impatto di un’incertezza, presente nella condizione iniziale, sulla soluzione dell’EDPS, nella seconda si analizzano gli impatti di una perturbazione dei termini funzionali dell’EDPS del coefficiente della funzione di Green associata. In entrambi i casi dimostriamo che lo sharp e la discrepanza sono soluzioni di due EDPS lineari dipendenti dalla soluzione dell’EDPS iniziale

Over the past several decades and increasingly in recent years, blood transfusions in the United States have plummeted as surgery has gotten more precise and less invasive. Alongside this decrease in general transfusions has been an increase in specific blood products for patients whose immune systems require special treatment. Simultaneously, trends in healthcare in the United States have incentivized regional hospitals to join large conglomerates. These coexisting factors have left regional blood banks, traditionally economically viable, in much weakened states. This thesis was born out of an initial curiosity to discover whether or not genetic science, and genotyping in particular, could benefit small regional blood banks by allowing them to bring down their costs of pre-transfusion blood testing or offer new products. I focus on the San Diego Blood Bank (SDBB) as a case study of the larger blood banking industry. In the course of this research, economic factors were taken into consideration as well as social and health. A minor question that was also discussed was whether genotyping not only help regional blood banks survive fiscally but also open the gateway to better patient outcomes and lower costs nationally of blood transfusions and their associated costs. Feasibility analyses and financial modeling suggest support for genotyping blood donors and transfusion recipients in order to more perfectly match blood transfusions through extended antigen matching.

L'obiettivo della tesi è lo sviluppo e nell'analisi di un modello macro-finanziario con aspetti reali e finanziari dell'economia, nell'ottica di ottenere un quadro comprensivo per l'analisi del rischio sistemico e delle instabilità. Il primo capitolo verte sulla costruzione di un modello ad agenti che si caratterizza per la presenza del mercato dei beni, del credito, del lavoro e interbancario. Il modello riproduce fluttuazioni endogene ed è in grado di replicare alcuni fatti stilizzati riguardanti i cicli economici e creditizi, mentre il mercato interbancario ha un ruolo importante dal punto di vista della stabilità e dell'efficienza. In particolare la regolazione prudenziale combinata con le aspettative adattive può esacerbare il comportamento precauzionale delle banche durante una recessione, inducendo a trattenere liquidità anche le banche solide. Inoltre la connettività del mercato interbancario ha un duplice effetto: da un lato favorisce l'accesso al credito nell'economia reale, dall'altro accresce l'accumulo di liquidità. Il secondo capitolo si concentra su un insieme di esperimenti condotti tramite il modello precedentemente sviluppato. Lo scopo è di confrontare tra loro politiche macro-prudenziali in cui le banche sono soggette a requisiti minimi di capitale derivati da misure di rischio sistemico. Nello specifico gli indicatori di rischio sistemico sono suddivisi in misure di mercato e di rete. Ogni categoria è ulteriormente scomposta in misure di vulnerabilità e misure di impatto. I risultati rivelano che le politiche costruite su indicatori di vulnerabilità sono migliori di quelle basate sull'impatto, dato che riducono i fallimenti da contagio senza peggiorare la performance macroeconomica. / The purpose of the thesis is to develop and analyse a macro-financial model with real and financial aspects of the economy to obtain a comprehensive framework for the analysis of systemic risk and instabilities. The first chapter concerns the construction of an agent-based-model, whose characteristic is the presence of goods, credit, labour and interbank markets. The model reproduces endogenous business cycles and it is able to replicate some stylized facts about business and credit cycles, while the interbank market has an important role for stability and efficiency. In particular prudential regulation, combined with adaptive expectations can exacerbate the precautionary behaviour of banks during a recession, inducing liquidity hoarding by sound banks. Furthermore connectivity of the interbank market has a twofold effect: on one side it supports credit to the real economy, on the other it increases liquidity hoarding. The second chapter is focused on a set of policy experiments performed performed on the model previously developed. The aim is to compare different macroprudential policies where banks are subject to minimum capital requirements derived from systemic risk measures. In detail systemic risk indicators are divided in market-based and network based measures. Each class is further decomposed in measures of vulnerability and measures of impact. The results reveal that policies based on vulnerability indicators perform better than those based on impact, reducing contagious defaults without worsening the macroeconomic performance.

В работе описаны сервисные бизнес-модели, разработаны электронные инструменты для выявления основных рисковых факторов проекта. На примере высокорискованого проекта по внедрению цифровой платформы структурированы основные факторы развертывания проекта. Проведена апробация применения карты стресс-тестирования проекта. Составлен алгоритм получения одновременно нескольких решений для различных условий проекта. / The paper describes service business models and developed electronic tools to identify the main risk factors of the project. Using the example of a high-risk project to implement a digital platform, the main factors of project deployment are structured. The application of the project stress testing map was tested. An algorithm has been compiled for obtaining several solutions simultaneously for various project conditions.

This thesis is about the problems of PPP projects. These are the projects, whose realization is based on the partnership of the private and public sector. This way brings new possibilities how is building and management of public infrastructure more effective. In theoretical part the basic information concerning the problems of PPP projects is described, its advantages and disadvantages, basic characters and principles. In this thesis is described actual state of PPP projects in the Czech Republic. In practical part the thesis is about specific concession project, whose realization is considered. It is the project of construction and operation of cableway to Spilberk Castle. Within this part at first the entrance data for financial models have been found, after that the financial models have been count and the analysis of sensitivity has been finished. In conclusion the evaluation of project has been done and there was the recommendation how to realize the project.