Includes bibliographical references / The central idea of the theory of storage is that the level of inventory influences the effect that changes in the demand-and-supply conditions have on spot and futures prices. With the use of monthly data for the period January 1992 to January 2010, I find that the predictions of the theory of storage do not always hold in the platinum market. In conflict with the theoretical predictions, I find that: i) demand-and-supply shocks will have the same effect on spot and futures prices, regardless of the level of inventory; and ii) changes in spot prices have very similar effects on the changes in futures prices when inventory is high and when it is low. In support of the theory of storage, I find a significant negative correlation between the volatility of spot prices and inventory throughout the sample period. Thereafter, I test the forecasting ability of the spot price volatility by employing a GARCH-t(1,1) model and find that volatility can be forecast fairly accurately for short periods, during which the spot prices are somewhat stable.

In the past two decades Mathematical Programming has come to occupy a place of importance in Economic Studies and in Operations Research. Roughly speaking, Mathematical Programming is the analysis of problems of the type: "Find the maximum of a function, when the variables are subject to inequality and equality constraints". The term "Linear Programming" corresponds to the case where, the function to be maximized (the so called objective function) and the equality and inequality constraints are linear. The term "Non-Linear Programming" should then become self-defined. With the introduction of Dantzig's Simplex Method, Linear Programming has become an everyday technique. The same, we regret to say, is not true for Nonlinear Programming because this subject is broader and much more difficult to unify than that of Linear Programming. In fact at present there does exist any unifying theory for Nonlinear Programming. However, we feel that research on this field is gathering tremendous momentum and that in the not too distant future Nonlinear Programming will become both a practical and fundamental tool in many spheres of Science. One of the subject matters of Nonlinear Programming is what we came to call "Quadratic Programming". This name is restricted to the specific problem of maximizing or minimizing a quadratic objective function f(X) = CX + X'DX, where CX is a linear form and X'DX a quadratic form, subject to linear constraints. Historically, Quadratic Programming was the first venture into the theory of Nonlinear Programming. More specifically it is the purpose of this thesis to: (i) Present a unified and simple treatment of the Theory of Concave (Convex) Quadratic Programming (in no way will mathematical rigour be sacrificed for simplicity). (ii) Present a collection of "Simplicial Methods" for solving quadratic programming problems, which are but extensions of the Simplex Method ( for Linear Programming, whose "accuracy" and "convergence" make them completely self-sufficient for the solution of any type of concave (convex) quadratic programming problems.

This dissertation analyses ex-ante asymmetric performance fee structures used by South African Mutual Funds and estimates performance fees some time before the fees are paid. Certain parties might benefit from having a reasonable estimate of its value. We use spread option theory to value ex-ante performance fees. The data consist of monthly benchmark and fund gross returns from December 1999 to October 2014. The theoretical value of ex-ante performance fees is a function of spread volatility, therefore high spread volatilities give rise to high ex-ante performance fees. Ex-ante performance fee estimates are highly sensitive to the correlation between the fund and benchmark and a low positive correlation gives rise to a high ex-ante performance fee. The distribution of ex-ante performance fees is positively skewed because of the maximum function in the payoff. Ex-ante performance fee estimates obtained are lower than the actual performance fees paid.

Includes bibliographical references. / The objective of this dissertation is to develop and test an investment process for hedge fund of funds (HFoFs) in South Africa. The dissertation proposes a three tiered process, adapted from the works of Lo (2008). Step one of the proccess involves the categorisation of hedge funds into broadly defined groups based on predefined factors. Two classification methodologies are examined herein to determine optimal category definitions. These are 1) an adaption of the classification developed by Schneeweis and Spurgin (2000), based on the correlation of hedge funds to an appropriate benchmark and the returns offered by these hedge funds, and 2) classification by cluster analysis. Once a finite set of classification is defined, step two of the process uses a minimum variance optimisation, based on forward-looking parameter estimates of return and co-variance to compute the optimal capital allocation to these categories. The final stage of the process employs a mixture of quantitative and qualitative analysis to allocate capital within categories to individual hedge funds.

A currency trio is a set of three currencies and their respective exchange rates, which have a relationship fixed by a triangular arbitrage condition. This condition forms the basis for the derivation of a geometric interpretation of the relationships between the exchange rates. In the geometric framework, the three currencies in a currency trio are represented by a triangle, where each of the vertices represents a currency. The volatilities of the exchange rates are represented by the lengths of the sides joining the respective currencies and the cosine of each angle represents the correlation between the two exchange rates depicted by the angle's adjacent sides. The geometric approach is particularly useful when dealing with implied data as it allows the calculation of implied correlation using implied volatility. This is valuable as implied volatility is frequently quoted in the foreign exchange market; whereas, implied correlation is not directly quoted and is more difficult to extract from market data. This dissertation aims to thoroughly investigate the geometric framework and use it to visualise and interpret the relationships between currencies in a currency trio. The analysis will initially look at currency trios with realised spot data before moving on to implied data. In the implied data context, the framework will be used to extract and evaluate implied correlation estimates using implied volatility data extracted from the foreign exchange market. The framework will be extended to investigate whether an illiquid option can be proxy hedged using options on the two other currencies in a currency trio. Finally, the findings will be discussed and the feasibility of the applications of the framework will be considered.

Fourier methods form an integral part in the universe of option pricing due to their speed, accuracy and diversity of use. Two types of methods that are extensively used are fast Fourier transform (FFT) methods and the Fourier-cosine series expansion (COS) method. Since its introduction the COS method has been seen to be more efficient in terms of rate of convergence than its FFT counterparts when pricing vanilla options; however limited comparison has been performed for more exotic options and under varying model assumptions. This paper will expand on this research by considering the efficiency of the two methods when applied to spread and worst-of rainbow options under two different models - namely the Black-Scholes model and the Variance Gamma model. In order to conduct this comparison, this paper considers each option under each model and determines the number of terms until the price estimate converges to a certain level of accuracy. Furthermore, it tests the robustness of the pricing methodologies to changes in certain discretionary parameters. It is found that although under the Black-Scholes model the COS method converges in fewer terms than the FFT method for both spread options (32 versus 128 terms) and the rainbow options (64 versus 512 terms), this is not the case under the more complex Variance Gamma model where the terms to convergence of both methods are similar. Both the methodologies are generally robust against changes in the discretionary variables; however, a notable issue appears under the implementation of the FFT methodology to worst-of rainbow options where the choice of the truncated integration region becomes highly influential on the ability of the method to price accurately. In sum, this paper finds that the improved speed of the COS method against the FFT method diminishes with a more complex model - although the extent of this can only be determined by testing for increasingly complex characteristic functions. Overall the COS method can be seen to be preferable from a practical point of view due to its higher level of robustness.

Includes abstract. / Includes bibliographical references (leaves 100-101). / The aim of the study is to ascertain whether the information gained from the more complicated multivariate matrix decomposition models can be used to better forecast the covariance matrix and produce a Value at Risk estimate which more appropriately describes fat-tailed financial time-series.

Includes bibliographical references (leaves 120-123) / In South Africa the exchange rate receives a large amount of attention, due to its volatility and its perceived effect on share returns. This dissertation examines the international literature regarding exchange rate exposure and replicates their methods in a South African context to determine the model that finds the most exchange rate exposure. With this model, and a few variations, the persistence of exchange rate exposure is examined, where it is found that a few shares consistently act as the best hedges against R/$ depreciation and similarly a few shares are consistently the best at exploiting Rand strength. With this in mind two hedging techniques are compared in their ability to protect against a R/$ depreciation, and simultaneously provide market related returns, against the ITRIX exchange traded fund. It was found that the methods were successful in that they were able to hedge against R/$ depreciation while still participating in the recent rapid growth on the J.S.E.

Skilled construction workers play a vital role in the delivery of construction projects. However, there has been report off their shortage within the Nigerian construction industry. The commitment of the few available ones to their organisation is therefore important as this is bound to influence the service delivery of these organisations. It is based on this knowledge that this study assessed the commitment of skilled construction workers in Abuja, Nigeria. The study adopted a survey design and quantitative data were gathered from skilled construction workers in registered construction companies in the study area. Percentage, mean item score, and Kruskal-Walis H-Test were used in analysing the data gathered. The study revealed that the type of employment of skilled workers (full time, part-time or contract) has no significant relationship with their commitment type. The common type of commitment exhibited is the continuance commitment. The most significant factors influencing their commitment are; getting feedback from supervisors, payment received being equal to work done, and availability of opportunities to grow. The practical implication of this result is that construction companies within the country need to improve in the aspect of human resource management so as to attain better commitment and at the same time improve their productivity. It is believed that the findings of this study will assist construction organisations in making appropriate planning and developing significant methods that will assist them in enhancing their organisational commitment of their skilled workers, and by so doing increasing organisational performance and workers productivity.

Includes bibliographical references. / The causes of the 2008 financial crisis were wide ranging. Some financial commentators have suggested there were significant inadequacies in the models used to price complex derivatives such as synthetic Collaterilised Debt Obligations (CDOs). We discuss the technical properties of CDOs and the modeling approaches used by CDO traders and the watchdog credit rating agencies. We look at how the pricing models fared before and during the financial crisis. Comparing our model prices to market synthetic CDO prices, we investigate how well these pricing models captured the underlying financial risks of trading in CDOs.