This thesis deals with interest rate swaps. In addition to chapters on basic principles of interest rate swaps also provides insight into the current situation in the derivative markets. The main part is devoted to the valuation of interest rate swaps, where is in addition to the theoretical site also solved the problem of obtaining the necessary data for calculations in practice. The conclusion of this work is devoted to two practical examples, which are dealing with the problem of the valuation of interest rate swaps.

In mathematical finance, the sensitivities of option prices to various market parameters, also known as the “Greeks”, reflect the exposure to different sources of risk. Computing these is essential to predict the impact of market moves on portfolios and to hedge them adequately. This is commonly done using Monte Carlo simulations. However, obtaining accurate estimates of the Greeks can be computationally costly. Multilevel Monte Carlo offers complexity improvements over standard Monte Carlo techniques. However the idea has never been used for the computation of Greeks. In this work we answer the following questions: can multilevel Monte Carlo be useful in this setting? If so, how can we construct efficient estimators? Finally, what computational savings can we expect from these new estimators? We develop multilevel Monte Carlo estimators for the Greeks of a range of options: European options with Lipschitz payoffs (e.g. call options), European options with discontinuous payoffs (e.g. digital options), Asian options, barrier options and lookback options. Special care is taken to construct efficient estimators for non-smooth and exotic payoffs. We obtain numerical results that demonstrate the computational benefits of our algorithms. We discuss the issues of convergence of pathwise sensitivities estimators. We show rigorously that the differentiation of common discretisation schemes for Ito processes does result in satisfactory estimators of the the exact solutions’ sensitivities. We also prove that pathwise sensitivities estimators can be used under some regularity conditions to compute the Greeks of options whose underlying asset’s price is modelled as an Ito process. We present several important results on the moments of the solutions of stochastic differential equations and their discretisations as well as the principles of the so-called “extreme path analysis”. We use these to develop a rigorous analysis of the complexity of the multilevel Monte Carlo Greeks estimators constructed earlier. The resulting complexity bounds appear to be sharp and prove that our multilevel algorithms are more efficient than those derived from standard Monte Carlo.

Pour remédier aux nombreuses insuffisances et défaillances constatées dans le système de régulation et de surveillance du secteur financier, post crise, de nombreuses réformes institutionnelles ont été réalisées à l'initiative des organismes et autorités de régulation bancaire et financière aussi bien au niveau national qu'au niveau international. Le Royaume du Maroc, en vertu de son statut avancé, signé en octobre 2008, a fait un réel effort pour réduire les différences entre les législations marocaine et européenne. Il a consenti à se rapprocher des normes européennes sur le plan législatif et réglementaire avec l'objectif d'être intégré au marché intérieur européen et de disposer d'une économie plus efficace. Toutefois, le système bancaire marocain ne semble pas adhérer aux changements induits par ce travail de convergence, si non il y a encore du chemin à faire dans ce sens et une convergence totale demandera, incontestablement, "des années"! Cette thèse tente d'examiner les difficultés d'adaptation des techniques de régulation européenne au système financier marocain à travers notamment, le système de régulation des banques marocaines, l'encadrement des mécanismes relevant du shadow banking et des opérations du marché des produits dérivés. Elle met l'accent sur les nombreux défis que cette industrie aura à relever dans les années à venir. Après une analyse des principales difficultés d'adaptation des techniques de régulation européennes au système financier marocain (Partie I), quelques solutions sont proposées, à savoir la finance islamique comme une finance complémentaire à la finance conventionnelle, l'inclusion financière comme une solution ayant pour finalité la réduction de la pauvreté et la création de postes d'emplois et le crowdfunding comme moyen de financement par le public de projet de création d'entreprise et solution au resserrement de crédit constaté après la crise de 2008 (Partie II). / The extent of the 2008 financial crisis' diffusion gave rise to strenuous and far-reaching debates about international financial stability. In fact, the question of financial instituions' social responsability seen as a financial stability vector has become the center of every debate. Financial instituions' governance and risk management devices have not only highlighted the vulnerability of the banking system, but also its inability to deal with liquidity requirements. With no doubt,banks have not been cautions enough to evaluate the risks they were taking. After the crisis, many institutional reforms were carried out at the initiative of banking and financial regulatory authorities, both at national and international levels, to tackle the numerous shortcomings and deficiencies found in the financial sector's regulation and supervision system. Under the Advanced Status, signed in October 2008, the Kingdom of Morocco has tried hard to reduce the gap between the Moroccan and the European legislations. In fact, it has agreed to move closer to European standards on the legislative and regulatory level aiming to be more integrated into the European internal market and to have a more efficient economy. Nevertheless, the banking system doesn't seem to adhere to the changes that were induced by this convergence work. Thus, there is still some way to go in this direction, not to mention that such a total convergence would take "years"! This thesis attempts to examine the difficulties of adapting European regulatory techniques to the Moroccan financial system, particularly through the Moroccan banks' control system and the supervision of mechanisms that take place under the "Shadow Banking" and the derivative market. It emphasizes all of the challenges this industry will have to face in the coming years. After an analysis of the main difficulties of adapting European regulatory techniques to the Moroccan financial system (Part I), some solutions are suggested,namely Islamic finance as a complement to the conventional one, financial inclusion as a solution aiming to reduce poverty and create jobs, and "Crowdfunding" as a financing tool for the mass individual investors to back start up projects, and a solution to the credit tightening phenomenon after the crisis of 2008 (Part II).

This thesis evaluates and constructs a general, product-neutral legal concept and model of financial instruments, as opposed to the product-dependent definitions currently employed in contemporary capital markets law. Through a combination of law and economics perspectives, legal history, and comparative analysis, the study examines the various types of financial instruments currently and previously in use. The legal characteristics and features of these instruments are evaluated and compared, leading to the identification of commonalities that can be used to define a product-neutral concept. The thesis argues that such a concept is more beneficial to the function of the capital markets by removing obstacles for financial innovation while also providing a consistent way to ensure that new financial products are governed by the same regulatory framework as comparable instruments.The thesis also examines the historical evolution of financial instruments and how it has been driven by the evolution of international trade and the demand and surplus of available capital. The proposed concept is applied to current financial instruments, including equity and debt, as well as pre-modern markets, and evaluated in terms of regulation, practical use, and legal characteristics such as transferability and negotiability.The research of this thesis encountered several challenges and limitations. Firstly, the historical and comparative analysis proved difficult to carry out, due to limitation in available source material and language related restrictions, respectively. These limitations were overcome by limiting the scope and by employing contacts with law firms in the respective jurisdictions. Secondly, several key issues proved to require further research to be able to provide definitive conclusions. Such research would have been out of scope and as such, simplified explanations and models were employed. The thesis concludes with a discussion of the practical implications of the proposed concept, including its application to cryptocurrencies and similar assets, and identifies potential areas for future research.