With the exception of holders of default-free instruments, a key risk run by investors is credit risk. To meet the need of investors to hedge this risk, the market uses credit derivatives. The South African credit derivatives market is still in its infancy and only the very simplistic instruments are traded. One of the reasons is due to the technical sophistication required in pricing these instruments. This dissertation introduces the key concepts of risk neutral probabilities, arbitrage free pricing, martingales, default probabilities, survival probabilities, hazard rates and forward spreads. These mathematical concepts are then used as a building block to develop pricing formulae which can be used to infer valuations to the most popular credit derivatives in the South African financial markets. / Operations Research / M.Sc. (Operations Research)

There are two transport systems used by agricultural businesses engaged in primary production. These are transport systems involving tractors and motorized vehicles. Transport systems involving tractors are made up of motorized vehicles and vehicles that are Toled Grand Super , or more specifically, a motor vehicle plus one or more vehicles that are towed along. A motorized vehicle refers to an agricultural traktor John Deere 6620. Motorized transport systems are comprised of Lorries Tatra 815 Agro. A lorry can only have one additional vehicle connected to itself. The transport systems mentioned above can be used in agricultural businesses engaged in primary production along with similar or identical productions. Motorized transport systems used in agricultural primary production are in the majority of cases applied to additional productions. This is the given transport system framework, which can be setup with adaptations for various uses. It therefore follows that the possibilities of comparing transport systems using universal undercarriages are increased. Expenditure associated with these transport systems, are easily compared. It is also possible to easily compare transport systems involving tractors with motorized transport systems as long as there is no need for more vehicles connected to them. It is obvious that the use of motorized transport systems for longer distances is preferable to transport systems involving tractors. Expenses for every driven kilometre with the comparable transport systems show a significant difference in cost. This difference is 36,85 Kč. On the other hand, it is preferable to use tractors for shorter distances involving a larger amount of material. he cost of one tonne of material transported is different about 11,55 Kč.

Submitted by Daniel Benabou (dbenabas@gmail.com) on 2018-09-24T14:05:05Z No. of bitstreams: 1 Daniel Benabou - Final.pdf: 1509370 bytes, checksum: b5f974a956000f0474b19f3aa92f13db (MD5) / Approved for entry into archive by Joana Martorini (joana.martorini@fgv.br) on 2018-09-24T15:01:39Z (GMT) No. of bitstreams: 1 Daniel Benabou - Final.pdf: 1509370 bytes, checksum: b5f974a956000f0474b19f3aa92f13db (MD5) / Approved for entry into archive by Isabele Garcia (isabele.garcia@fgv.br) on 2018-09-24T20:11:14Z (GMT) No. of bitstreams: 1 Daniel Benabou - Final.pdf: 1509370 bytes, checksum: b5f974a956000f0474b19f3aa92f13db (MD5) / Made available in DSpace on 2018-09-24T20:11:14Z (GMT). No. of bitstreams: 1 Daniel Benabou - Final.pdf: 1509370 bytes, checksum: b5f974a956000f0474b19f3aa92f13db (MD5) Previous issue date: 2018-08-24 / Com o objetivo de obter a estrutura de curvas futuras de swaps de energia, este trabalho foca na implementação numérica do modelo de Heath, Jarrow e Morton (1992) utilizando somente as informações dos contratos de swaps negociados no Sistema Elétrico Brasileiro, através do modelo discreto do HJM conhecido como Modelo de Brace, Garatek e Musiela (1997), também referido como Modelo de Mercado. A estrutura de volatilidade foi obtida de forma não-paramétrica através de curvas suaves e de vértices sintéticos obtidos por interpolação dos dados de venda de uma comercializadora tratados através do método de Análise de Componentes Principais (PCA). Os dados analisados foram contratos firmados entre o início de 2013 e o primeiro quadrimestre de 2015. / For the purpose of obtaining the structure of future swap energy curves in the Brazilian market, this paper focuses on the numerical implementation of the Heath, Jarrow and Morton model (1992) using market information regarding the swap contracts traded in the Brazilian energy system, with its multi-factor discrete form, the Brace, Garatek and Musiela (1997) model, also known as Market Model. The volatility structure is obtained with smooth curves and synthetic vertices, obtained thru swap contracts negotiated by a Brazilian energy trading company. Also, the volatility structures where analyzed with the Principal Components Analysis (PCA). The analyzed data where swap contracts stablished between the beginning of 2013 until the first quarter of 2015.

The main task of the diploma thesis is an analysis of financial performance and position of Morgan Stanley during several successive periods before and during the subprime financial crisis. Through the analysis of trends in key items, it also demonstrates strong cyclicality of financial performance and position of the investment bank. The first chapter deals with history and key divisions of the Company. The following chapter generally discusses selected phenomena, which, as per the author's view, significantly influenced industry-wide record-breaking performance during the period before the subprime crisis, and which substantially determined Morgan Stanley's risk profile and performance's corrections later during the Crisis. The core part of the Thesis is conceived as an analysis of financial performance and position of Morgan Stanley during the selected periods. The analysis of pre-crisis period until 2006 in the third chapter demonstrates growth of activities lying behind the unprecedented profitability of the Institution. The following fourth chapter analyzes deteriorating financial performance during the subprime crisis and indicates crucial strategy changes, implemented by the Company at the end of 2008. Effects of the strategic changes and challenges of the future development of the Institution are discussed in the last chapter. Additionally, the Thesis includes annexes, which further deal with selected topics and their general relations to investments banks and two annexes which compare Morgan Stanley with its nearest peers during specific periods.

Land use transition in dryland ecosystems is one of the major driving forces to landscape change that directly impacts the welfare of humans. In this study, the support vector machine (SVM) classification algorithm and cross tabulation matrix analysis are used to identify systematic and random processes of change. The magnitude and prevailing signals of land use transitions are assessed taking into account net change and swap change. Moreover, spatiotemporal patterns and the relationship of precipitation and the Normalized Difference Vegetation Index (NDVI) are explored to evaluate landscape degradation. The assessment showed that 44% of net change and about 54% of total change occurred during the study period, with the latter being due to swap change. The conversion of over 39% of woodland to cropland accounts for the existence of the highest loss of valuable ecosystem of the region. The spatial relationship of NDVI and precipitation also showed R2 of below 0.5 over 55% of the landscape with no significant changes in the precipitation trend, thus representing an indicative symptom of land degradation. This in-depth analysis of random and systematic landscape change is crucial for designing policy intervention to halt woodland degradation in this fragile environment.

This Diploma Thesis is dedicated to stress analysis of carrier swap bodies Mega 25 with maximum technical weight 27 000 kg and has been worked out in corporation with ZDT Nové Veselí company. The aim of this work is to stress analysis of trailer in various burdensome conditions. The first section of the Thesis is occupied with original design and burdensome condition. Then, according to these states gained strength to control the finite element method, implement and then modify the design including design of new drawbar and then create selected construction drawings prepared.

With the substantial size of the interest rate markets, the importance of accurate pricing, risk measurement and performance attribution can not be understated. However, the models used on the markets often have underlying issues with capturing the market's fundamental behavior. With this thesis, we aim to improve the pricing, risk measurement, and performance attribution of interest rate swap portfolios. The paper is divided into six main parts, by subject, to aid in achieving these goals. To begin with, we validate all cash flows with SEB to increase the validity of the results. Next, we implement an optimization-based model developed by Jörgen Blomvall to estimate multiple yield curves.  By considering innovations of the daily in-sample curves, risk factors are computed with principal component analysis. These risk factors are then used to simulate one-day and ten-day ahead scenarios for the multiple yield curves using a Monte Carlo method. Given these simulated scenarios, risk measures are then computed. When backtested, these risk measurements give an indication on the overall accuracy of the methodology, including the estimated curves, the derived risk factors, and the simulation methodology. Along with the simulation, on each out-of-sample day, monetary performance attribution for the portfolios is also performed. The performance attribution indicates what drives the value change in the portfolio. This can be used in order to evaluate the estimated yield curves and derived risk factors. The risk measurement and performance attribution is done for three different portfolios of interest rate swaps on the EUR, USD, and SEK markets. However, the risk factors are only estimated for EUR data and used for all portfolios.  The main difference to previous work in this area is that, for all implementations, a multiple yield curve environment is studied. Different PCA algorithms are evaluated to increase the precision and speed of the risk factor calculation. Mean reverting risk factors are developed in the simulation framework, along with a Latin hypercube sampling method accounting for dependence in the random variables to reduce variance. We also study the EUR and SEK markets, while the focus in previous literature is on the USD market. Lastly, we calculate and backtest the risk measures value-at-risk and expected shortfall for one-day and ten-day horizons. Four different PCA methods are implemented, a bidiagonal divide and conquer SVD algorithm, a randomized SVD method, an Arnoldi method, and an optimization-based PCA algorithm. We opt to use the first one due to high accuracy and the ability to calculate all eigenpairs. However, we recommend to use the Arnoldi method in future implementations and to further study the optimization-based method. The Latin hypercube sampling with dependence method is able to produce random variables with the same correlation as the input variables. In the simulation, we are able to produce results that pass all backtests for the risk measures considering the USD portfolio. For the EUR and SEK portfolios, it is shown that the risk measures are too conservative. The results of the mean reversion method indicate that it produces slightly less conservative estimates for the ten-day horizon. In the performance attribution, we show that we are able to produce results with small error terms, therefore indicating accurately estimated term structures, risk factors, and pricing. We conclude that we are partly able to fulfill the stated purpose of this thesis due to having produced accurate pricing and satisfactory performance attribution results for all portfolios, and stable risk measures for the USD portfolio. However, it is not possible to state with certainty that improved risk measurements have been achieved for the EUR and SEK portfolios. Although, we present several alternative approaches to remedy this in future implementations.

Depuis la succession des récentes crises financières, les « dérivés de crédit » connaissent une notoriété médiatique très intense qui dépasse la seule sphère des spécialistes. Créés au début des années 1990, ils sont des instruments financiers de transfert du risque de crédit. Ils autorisent tant la protection que la spéculation. Ils sont juridiquement documentés par des conventions-Cadres proposées par l’International Swaps and Derivatives Association (ISDA), et dans une très petite mesure, par la Fédération Bancaire Française en France. Ils regroupent cinq grandes catégories de contrat : « credit default swap » ou « contrat d’échange sur le risque de crédit », « credit linked notes » ou « dérivé de crédit titrisé », « credit spread option » ou « option sur écart de taux », « credit spread forward » ou « dérivé sur écart de taux » et « total rate of return swap » ou « dérivé de transfert total de rendement ». La nature et la diversité des « dérivés de crédit » posent depuis toujours de sérieuses difficultés de qualification dans de nombreux pays. En droit français, si une qualification commune semble émerger, celle d’instrument financier, elle est hélas insuffisante à apporter un régime juridique complet. Un travail complémentaire de qualification est indispensable pour chaque contrat membre des « dérivés de crédit ». / Nowadays, since financial crisis, « credit derivatives » are famous. Born in 1990’s, they transfer the credit risk. They are speculation’s instrument or margin’s instrument. International Swaps and Derivatives Association (ISDA), and the Fédération Bancaire Française (in France), point to pattern juridical agreement. Credit derivatives include five big sort of agreement : « credit default swap » (« contrat d’échange sur le risque de crédit »), « credit linked notes » (« dérivé de crédit titrisé »), « credit spread option » (« option sur écart de taux »), « credit spread forward » (« dérivé sur écart de taux ») and « total rate of return swap » (« dérivé de transfert total de rendement »). Their variety and essence ask difficult question of juridical appreciation in many countries. In French law, credit derivatives are « instrument financier ». But this juridical appreciation is incomplete. Every sort of agreement must being individually studies.

許多公司在發行公司債的時候，會給此公司債一個可提前贖回的特性，此種公司債稱為可贖回公司債(Callable Bond)，用來規避利率變動風險的金融商品也與我們熟知的利率交換不同，稱為可取消利率交換(Cancelable Swap)。其實可取消利率交換可以拆解成百慕達利率交換選擇權(Bermudan Swaption)加上利率交換，由於利率交換之評價較簡單也有市場一致的評價方法，因此百慕達利率交換選擇權便成為評價的重點。 評價的部分，由於百慕達式的商品有提前履約的特性，造成其封閉解不存在，因此需要利用其他的近似解或是數值方法來求它的價格。由於本文採用BGM(1997)的市場利率模型(Libor Market Model)，其高維度的性質導致數狀方法與有限差分法使用起來較無效率，因此本文選擇使用蒙地卡羅法做為評價的方法，同時利用Longstaff and Schwartz(2001)的最小平方蒙地卡羅法(Least Squares Monte Carlo Method)來解決提前履約的問題。 最後，本文將採用2種利率波動度假設與2種不同利率間相關係數的假設，共4種組合，在歐式利率交換選擇權的市場波動度下進行校準，使用校準出來的參數進行評價來得到4種價格。再進行商品的敏感度分析(Sensitivity Analysis)和風險值(Value at Risk)的計算。

Subprime residential mortgage loan securitization and its associated risks have been a major topic of discussion since the onset of the subprime mortgage crisis (SMC) in 2007. In this regard, the thesis addresses the issues of subprime residential mortgage loan (RML) securitization in discrete-, continuous-and discontinuous-time and their connections with the SMC. In this regard, the main issues to be addressed are discussed in Chapters 2, 3 and 4. In Chapter 2, we investigate the risk allocation choices of an investing bank (IB) that has to decide between risky securitized subprime RMLs and riskless Treasuries. This issue is discussed in a discrete-time framework with IB being considered to be regret- and risk-averse before and during the SMC, respectively. We conclude that if IB takes regret into account it will be exposed to higher risk when the difference between the expected returns on securitized subprime RMLs and Treasuries is small. However, there is low risk exposure when this difference is high. Furthermore, we assess how regret can influence IB's view - as a swap protection buyer - of the rate of return on credit default swaps (CDSs), as measured by the premium based on default swap spreads. We find that before the SMC, regret increases IB's willingness to pay lower premiums for CDSs when its securitized RML portfolio is considered to be safe. On the other hand, both risk- and regret-averse IBs pay the same CDS premium when their securitized RML portfolio is considered to be risky. Chapter 3 solves a stochastic optimal credit default insurance problem in continuous-time that has the cash outflow rate for satisfying depositor obligations, the investment in securitized loans and credit default insurance as controls. As far as the latter is concerned, we compute the credit default swap premium and accrued premium by considering the credit rating of the securitized mortgage loans. In Chapter 4, we consider a problem of IB investment in subprime residential mortgage-backed securities (RMBSs) and Treasuries in discontinuous-time. In order to accomplish this, we develop a Levy process-based model of jump diffusion-type for IB's investment in subprime RMBSs and Treasuries. This model incorporates subprime RMBS losses which can be associated with credit risk. Furthermore, we use variance to measure such risk, and assume that the risk is bounded by a certain constraint. We are now able to set-up a mean-variance optimization problem for IB's investment which determines the optimal proportion of funds that needs to be invested in subprime RMBSs and Treasuries subject to credit risk measured by the variance of IE's investment. In the sequel, we also consider a mean swaps-at-risk (SaR) optimization problem for IB's investment which determines the optimal portfolio which consists of subprime RMBSs and Treasuries subject to the protection by CDSs required against the possible losses. In this regard, we define SaR as indicative to IB on how much protection from swap protection seller it must have in order to cover the losses that might occur from credit events. Moreover, SaR is expressed in terms of Value-at-Risk (VaR). Finally, Chapter 5 provides an analysis of discrete-, continuous- and discontinuous-time models for subprime RML securitization discussed in the aforementioned chapters and their connections with the SMC. The work presented in this thesis is based on 7 peer-reviewed international journal articles (see [25], [44], [45], [46], [47], [48] and [55]), 4 peer-reviewed chapters in books (see [42], [50j, [51J and [52]) and 2 peer-reviewed conference proceedings papers (see [11] and [12]). Moreover, the article [49] is currently being prepared for submission to an lSI accredited journal. / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2010.