Corn production is scattered geographically over various continents, but most of it is grown in the United States. As such, the world price of corn futures contracts is largely dominated by North American corn prices as traded on the Chicago Board of Trade. In recent years, this market has been characterised by an increase in price volatility and magnitude of price movement as a result of decreasing stock levels. The development and implementation of an effective and successful derivative price risk management strategy based on the Chicago Board of Trade corn futures contract will therefore be of inestimable value to market stakeholders worldwide. The research focused on the efficient market hypothesis and the possibility of contesting this phenomenon through an application of a derivative price risk management methodology. The methodology is based on a combination of an analysis of market trends and technical oscillators with the objective of generating returns superior to that of a market benchmark. The study found that market participants are currently unable to exploit price movement in a manner which results in returns that contest the notion of efficient markets. The methodology proposed, however, does allow the user to consistently achieve returns superior to that of a predetermined market benchmark. The benchmark price for the purposes of this study was the average price offered by the market over the contract lifetime, and such, the efficient market hypothesis was successfully contested. / Business Management / D. Com. (Business Management)

This master thesis deals with the construction of a system for automatic classification of~unknown words based on derivation bonds. For this purpose, the system was designed to~extract derivative links based on electronic dictionaries and to create word-forming models from them. Based on this knowledge, it is then possible to incorporate unclassified words into existing nests formed from the obtained bonds, and their models, or create new ones. The reader will be gradually acquainted with the reasons that lead to the continuous transformation or expansion of the lexicon, the ways in which the words in~the~Czech language are derived and how to obtain information about the changes caused by this derivation process. This system builds on and extends the research of the branch of morphology in~the~project of a morphological analyzer of the Research Group of Knowledge Technologies, working at the Faculty of Information Technology of the Brno University of~Technology.

<div>In this thesis work, a novel approach for the design of a fractional order proportional integral</div><div>derivative (FOPID) controller is proposed. This design introduces a new time-varying FOPID controller</div><div>to mitigate a voltage spike at the controller output whenever a sudden change to the setpoint occurs. The</div><div>voltage spike exists at the output of the proportional integral derivative (PID) and FOPID controllers when a</div><div>derivative control element is involved. Such a voltage spike may cause a serious damage to the plant if it is</div><div>left uncontrolled. The proposed new FOPID controller applies a time function to force the derivative gain to</div><div>take effect gradually, leading to a time-varying derivative FOPID (TVD-FOPID) controller, which maintains</div><div>a fast system response and signi?cantly reduces the voltage spike at the controller output. The time-varying</div><div>FOPID controller is optimally designed using the particle swarm optimization (PSO) or genetic algorithm</div><div>(GA) to ?nd the optimum constants and time-varying parameters. The improved control performance is</div><div>validated through controlling the closed-loop DC motor speed via comparisons between the TVD-FOPID</div><div>controller, traditional FOPID controller, and time-varying FOPID (TV-FOPID) controller which is created</div><div>for comparison with all three PID gain constants replaced by the optimized time functions. The simulation</div><div>results demonstrate that the proposed TVD-FOPID controller not only can achieve 80% reduction of voltage</div><div>spike at the controller output but also is also able to keep approximately the same characteristics of the system</div><div>response in comparison with the regular FOPID controller. The TVD-FOPID controller using a saturation</div><div>block between the controller output and the plant still performs best according to system overshoot, rise time,</div><div>and settling time.</div>

Published Article / This study was conducted with 29 Grade 12 learners who were studying calculus. The purpose was to explore how the learners responded to questions based on the derivative and why they did so. Data was collected from the written responses of the learners to two assessments carried out over a six-month period as well as interviews with four of the learners. It was found that learners made extensive use of inappropriate formulae, drawn from other sections of the curriculum The study recommends that teachers should not focus solely on how to carry out procedures, but they should also pay attention to why certain procedures are appropriate or not.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This work employs perturbation techniques to price and hedge financial derivatives in a stochastic volatility framework. Fouque et al. [44] model volatility as a function of two processes operating on different time-scales. One process is responsible for the fast-fluctuating feature of volatility and corresponds to the slow time-scale and the second is for slowfluctuations or fast time-scale. The former is an Ergodic Markov process and the latter is a strong solution to a Lipschitz stochastic differential equation. This work mainly involves modelling, analysis and estimation techniques, exploiting the concept of mean reversion of volatility. The approach used is robust in the sense that it does not assume a specific volatility model. Using singular and regular perturbation techniques on the resulting PDE a first-order price correction to Black-Scholes option pricing model is derived. Vital groupings of market parameters are identified and their estimation from market data is extremely efficient and stable. The implied volatility is expressed as a linear (affine) function of log-moneyness-tomaturity ratio, and can be easily calibrated by estimating the grouped market parameters from the observed implied volatility surface. Importantly, the same grouped parameters can be used to price other complex derivatives beyond the European and American options, which include Barrier, Asian, Basket and Forward options. However, this semi-analytic perturbative approach is effective for longer maturities and unstable when pricing is done close to maturity. As a result a more accurate technique, the decomposition pricing approach that gives explicit analytic first- and second-order pricing and implied volatility formulae is discussed as one of the current alternatives. Here, the method is only employed for European options but an extension to other options could be an idea for further research. The only requirements for this method are integrability and regularity of the stochastic volatility process. Corrections to [3] remarkable work are discussed here. / AFRIKAANSE OPSOMMING: Hierdie werk gebruik steuringstegnieke om finansiële afgeleide instrumente in ’n stogastiese wisselvalligheid raamwerk te prys en te verskans. Fouque et al. [44] gemodelleer wisselvalligheid as ’n funksie van twee prosesse wat op verskillende tyd-skale werk. Een proses is verantwoordelik vir die vinnig-wisselende eienskap van die wisselvalligheid en stem ooreen met die stadiger tyd-skaal en die tweede is vir stadig-wisselende fluktuasies of ’n vinniger tyd-skaal. Die voormalige is ’n Ergodiese-Markov-proses en die laasgenoemde is ’n sterk oplossing vir ’n Lipschitz stogastiese differensiaalvergelyking. Hierdie werk behels hoofsaaklik modellering, analise en skattingstegnieke, wat die konsep van terugkeer to die gemiddelde van die wisseling gebruik. Die benadering wat gebruik word is rubuust in die sin dat dit nie ’n aanname van ’n spesifieke wisselvalligheid model maak nie. Deur singulêre en reëlmatige steuringstegnieke te gebruik op die PDV kan ’n eerste-orde pryskorreksie aan die Black-Scholes opsie-waardasiemodel afgelei word. Belangrike groeperings van mark parameters is geïdentifiseer en hul geskatte waardes van mark data is uiters doeltreffend en stabiel. Die geïmpliseerde onbestendigheid word uitgedruk as ’n lineêre (affiene) funksie van die log-geldkarakter-tot-verval verhouding, en kan maklik gekalibreer word deur gegroepeerde mark parameters te beraam van die waargenome geïmpliseerde wisselvalligheids vlak. Wat belangrik is, is dat dieselfde gegroepeerde parameters gebruik kan word om ander komplekse afgeleide instrumente buite die Europese en Amerikaanse opsies te prys, dié sluit in Barrier, Asiatiese, Basket en Stuur opsies. Hierdie semi-analitiese steurings benadering is effektief vir langer termyne en onstabiel wanneer pryse naby aan die vervaldatum beraam word. As gevolg hiervan is ’n meer akkurate tegniek, die ontbinding prys benadering wat eksplisiete analitiese eerste- en tweede-orde pryse en geïmpliseerde wisselvalligheid formules gee as een van die huidige alternatiewe bespreek. Hier word slegs die metode vir Europese opsies gebruik, maar ’n uitbreiding na ander opsies kan’n idee vir verdere navorsing wees. Die enigste vereistes vir hierdie metode is integreerbaarheid en reëlmatigheid van die stogastiese wisselvalligheid proses. Korreksies tot [3] se noemenswaardige werk word ook hier bespreek.

Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT : The standard-Heath–Jarrow–Morton (HJM) framework is well-known for its application to pricing and hedging interest rate derivatives. This study implemented the extended HJM framework introduced by Eberlein and Raible (1999), in which a Brownian motion (BM) is replaced by a wide class of processes with jumps. In particular, the HJM driven by the generalised hyperbolic processes was studied. This approach was motivated by empirical evidence proving that models driven by a Brownian motion have several shortcomings, such as inability to incorporate jumps and leptokurticity into the price dynamics. Non-homogeneous Lévy processes and the change of measure techniques necessary for simplification and derivation of pricing formulae were also investigated. For robustness in numerical valuation, several transform methods were investigated and compared in terms of speed and accuracy. The models were calibrated to liquid South African data (ATM) interest rate caps using two methods of optimisation, namely the simulated annealing and secant-Levenberg–Marquardt methods. Two numerical valuation approaches had been implemented in this study, the COS method and the fractional fast Fourier transform (FrFT), and were compared to the existing methods in the context. Our numerical results showed that these two methods are quite efficient and very competitive. We have chose the COS method for calibration due to its rapidly speed and we have suggested a suitable approach for truncating the integration range to address the problems it has with short-maturity options. Our calibration results provided a nearly perfect fit, such that it was difficult to decide which model has a better fit to the current market state. Finally, all the implementations were done in MATLAB and the codes included in appendices. / AFRIKAANSE OPSOMMING : Die standaard-Heath–Jarrow–Morton-raamwerk (kortom die HJM-raamwerk) is daarvoor bekend dat dit op die prysbepaling en verskansing van afgeleide finansiële instrumente vir rentekoerse toegepas kan word. Hierdie studie het die uitgebreide HJM-raamwerk geïmplementeer wat deur Eberlein en Raible (1999) bekendgestel is en waarin ’n Brown-beweging deur ’n breë klas prosesse met spronge vervang word. In die besonder is die HJM wat deur veralgemeende hiperboliese prosesse gedryf word ondersoek. Hierdie benadering is gemotiveer deur empiriese bewyse dat modelle wat deur ’n Brown-beweging gedryf word verskeie tekortkominge het, soos die onvermoë om spronge en leptokurtose in prysdinamika te inkorporeer. Nie-homogene Lévy-prosesse en die maatveranderingstegnieke wat vir die vereenvoudiging en afleiding van prysbepalingsformules nodig is, is ook ondersoek. Vir robuustheid in numeriese waardasie is verskeie transformmetodes ondersoek en ten opsigte van spoed en akkuraatheid vergelyk. Die modelle is vir likiede Suid-Afrikaanse data vir boperke van rentekoerse sonder intrinsieke waarde gekalibreer deur twee optimiseringsmetodes te gebruik, naamlik die gesimuleerde uitgloeimetode en die sekans-Levenberg–Marquardt-metode. Twee benaderings tot numeriese waardasie is in hierdie studie gebruik, naamlik die kosinusmetode en die fraksionele vinnige Fourier-transform, en met bestaande metodes in die konteks vergelyk. Die numeriese resultate het getoon dat hierdie twee metodes redelik doeltreffend en uiters mededingend is. Ons het op grond van die motiveringspoed van die kosinus-metode daardie metode vir kalibrering gekies en ’n geskikte benadering tot die trunkering van die integrasiereeks voorgestel ten einde die probleem ten opsigte van opsies met kort uitkeringstermyne op te los. Die kalibreringsresultate het ’n byna perfekte passing gelewer, sodat dit moeilik was om te besluit watter model die huidige marksituasie die beste pas. Ten slotte is alle implementerings in MATLAB gedoen en die kodes in bylaes ingesluit.

Thesis (LLM (Mercantile Law))--University of Stellenbosch, 2006. / The research defines derivatives as private contracts, with future rights and obligations imposed on all parties, used to hedge or transfer risk, which derives value from an underlying asset price or index, which asset price or index may take on various forms. The nature of derivatives is that the instruments are intended to be risk management tools. The objectives of derivatives are either to hedge a risk, or to speculate. Derivatives may be classified by the manner in which they are traded, either over the counter (OTC) or on exchange. Alternatively, derivatives may be classified on the basis of structure and mechanisms, i.e. forwards, futures, options or swaps. Risk and risk management are defined in the third chapter with the focus on merchant banking. The nature of risk is that it is inherent in all activities. The nature of risk management is that it aims to ensure that the risks faced by the merchant bank are managed on a daily basis. The objective of risk management is to ensure that losses are minimised and the appropriate level of risk is taken in order to maximise profits. Risk may be classified as operational, operations, market, systemic, credit and legal risk. A comprehensive discussion of credit risk is presented, as it pertains to the legal risk in derivatives in a merchant bank. This includes insolvency, set-off, netting, credit derivatives and collateral. Legal risk is defined as the risk of loss primarily caused by legal unenforceability (i.e. a defective transaction, for instance a contract), legal liability (i.e. a claim) or failure to take legal steps to protect assets (e.g. intellectual property). The nature of legal risk is that it is caused by jurisdictional and other cross-border factors, inadequate documentation, the behaviour of financial institutions, a lack of internal controls, financial innovation or the inherent uncertainty of the law. The objectives of legal risk management in derivatives are to avoid the direct and indirect costs associated with legal risk materialising. This includes reputational damage. Derivatives attract specific legal risks due to the complexity of the instruments as well as the constant innovation in the market. There remains some legal uncertainty regarding derivatives in terms of gaming, wagering and gambling, as well as insurance. The relationship between risk and derivatives is that due to the complexity and constant innovation associated with derivatives, there are some inherent risks to trading in derivatives. It is therefore important to ensure that there is a vested risk management culture in the derivatives trading environment. Chapter four gives an overview of derivatives legislation in foreign jurisdictions and in South Africa. The contractual and documentation issues are discussed with reference to ad hoc agreements, master agreements and ISDA agreements. The practical implementation issues of master agreements and ad hoc agreements are also discussed. The recommendations are that legal risk management be approached in a similar manner to credit, market and other risk disciplines. A legal risk management policy needs to be developed and implemented. The second recommendation is that a derivative to manage the legal risk in derivatives be developed.

This thesis is a technical inquiry into remedies for high inflation. In its center there is the usual tradeoff between inflation aversion on the one hand and some benefit from inflation via Phillips curve effects on the other hand. Most remarkable and pioneering work for us is the famous Barro-Gordon model - see (Barro & Gordon 1983a) respectively (Barro & Gordon 1983b). Parts of this model form the basis of our work here. Though being well known the discretionary equilibrium is suboptimal the question arises how to overcome this. We will introduce four different models, each of them giving a different perspective and way of thinking. Each model shows a (sometimes slightly) different way a central banker might deliver lower inflation than the one shot Barro-Gordon game at a first glance would suggest. To cut a long story short we provide a number of reasons for believing that the purely discretionary equilibrium may be rarely observed in real life. Further the thesis provides new insights for derivative pricing theories. In particular, the potential role of financial markets and instruments will be a major focus. We investigate how such instruments can be used for monetary policy. On the contrary these financial securities have strong influence on the behavior of the central bank. Taking this into account in chapters 3 and 4 we come up with a new method of pricing inflation linked derivatives. The latter to the best of our knowledge has never been done before - (Persson, Persson & Svenson 2006), as one of very view economic works taking into account financial markets, is purely focused on the social planer's problem. A purely game theoretic approach is done in chapter 2 to change the original Barro-Gordon. Here we deviate from a purely rational and purely one period wise thinking. Finally in chapter 5 we model an asymmetric information situation where the central banker faces a trade off between his current objective on the one hand and benefit arising from not perfectly informed agents on the other hand. In that sense the central bank is also concerned about its reputation.

Electro-Hydraulic (EH) systems are commonly used in the industry for applications that require high power-weight ratios and large driving forces. The EH system studied in this master thesis have recently been upgraded with new hardware components and as a part of this upgrade a new controller was requested. The system consists of a controller that computes a control signal for an electric motor. The motor drives a gear pump that generates a flow of hydraulic fluid. The flow is then directed to a cylinder. The movements of a piston in the cylinder is affected by the flow and the piston position can be measured. The measured piston position is then fed back to the controller and the control loop is complete. The system was previously controlled using a Proportional-Integral-Derivative (PID) controller and the purpose of this thesis is to compare the old controller with alternative control strategies suitable for this application. The evaluation of the controllers is based on both software and hardware simulations and results in a recommendation for final implementation of the best suited controller. The control strategies chosen for investigation are: a retuned PID controller, a PID controller with feed forward from reference, a PID based cascade controller, a Linear Quadratic (LQ) controller, and a Model Predictive Controller (MPC). To synthesize the controllers an approximate model of the system is formed and implemented in the software environment Matlab Simulink. The model is tuned to fit recorded data and provides a decent estimation of the actual system. The proposed control strategies are then simulated and evaluated in Simulink with the model posing as the real system. These simulations resulted in the elimination of the cascade controller as a possible candidate since it proved unstable for large steps in the reference signal. The remaining four controllers were all selected for simulation on the real hardware system. Unfortunately the MPC was never successfully implemented on the hardware due to some unknown compatibility error and hence eliminated as a possible candidate. The three remaining control strategies, PID, PID with feed forward from reference and the LQ controller, were all successfully implemented and simulated on hardware. The results from the hardware simulations compared to simulations made with the old controller, as well as the results from the software simulations, were then evaluated. Depending on the purpose one of two control strategies is recommended for this application. The LQ controller achieved the best overall performance and is presented as the control strategy best suited for this application.

Dans ce mémoire, nous traiterons du théorème de Lebesgue, un des plus frappants et des plus importants de l'analyse mathématique ; à savoir qu'une fonction à variation bornée est dérivable presque partout. Le but de ce travail est de fournir, à part la démonstration souvent proposée dans les cours de la théorie de la mesure, d'autres démonstrations élaborées avec des outils mathématiques plus simples. Ma contribution a consisté essentiellement à détailler et à compléter ces démonstrations, puis à inclure la plupart des figures pour une meilleure lisibilité. Nous allons maintenant, pour ce théorème qui se présente sous d'autres variantes, en proposer l'historique et trois démonstrations différentes. / In this dissertation, we will be handling a theorem of Lebesgue, one of the most stricking and ultimate of mathematical analysis ; namely a function with bounded variation has a derivative almost everywhere. The aim of our research is to provide, apart from the proof usually offered in measure theory courses, other demontrations achieved with more simple mathematical tools. My contribution was primarily to simplify and to complete these demonstrations, to include the most of the drawings in order to visualize what is being said. For this theorem, which has other presentations, we will give now the history and three different demonstrations.