Thesis (M.Sc.-Res.)--University of Wollongong, 2007. / Typescript. Includes bibliographical references: leaf 77-80.

Univ., Diss.--Tübingen, 1998. / A rev. version of the author's dissertation (doctoral--Tübingen). Includes bibliographical references. Literaturverz. S. [163] - 170.

Thesis (MComm (Mathematics))--University of Stellenbosch, 2007. / The word numéraire refers to the unit of measurement used to value a portfolio of assets. The change of numéraire technique involves converting from one measurement to another. The foreign exchange markets are natural settings for interpreting this technique (but are by no means the only examples). This dissertation includes elementary facts about the change of numeraire technique. It also discusses the mathematical soundness of the technique in the abstract setting of Delbaen and Schachermayer’s Mathematics of Arbitrage. The technique is then applied to financial pricing problems. The right choice of numéraire could be an elegant approach to solving a pricing problem or could simplify computation and modelling.

The payoff functions of contingent claims (options) of one variable are prominent in Financial Economics and thus assume a fundamental role in option pricing theory. Some of these payoff functions are continuous, piecewise-defined and linear or affine. Such option payoff functions can be analysed in a useful way when they are represented in additive, Boolean normal, graphical and linear form. The issue of converting such payoff functions expressed in the additive, linear or graphical form into an equivalent Boolean normal form, has been considered by several authors for more than half-a-century to better-understand the role of such functions. One aspect of our study is to unify the foregoing different forms of representation, by creating algorithms that convert a payoff function expressed in graphical form into Boolean normal form and then into the additive form and vice versa. Applications of these algorithms are considered in a general theoretical sense and also in the context of specific option contracts wherever relevant. The use of these algorithms have yielded easy computation of the area enclosed by the graph of various functions using min and max operators in several ways, which, in our opinion, are important in option pricing. To summarise, this study effectively dealt with maximum and minimum operators from several perspectives

Prof. F. Lombard

The net present value (NPV) approach has been widely accepted by corporate practitioners and academics as the principle tool for evaluating the feasibility of corporate financial investment opportunities. It conceptually provides an estimate in present value terms of a proposed investment's incremental contribution to the firm, enabling the company to pursue its goal of value maximization with more assurance. NPV uses a discount rate that in theory captures market risks. In the stable growth or mature industries, NPV works well. However, in high investment/high risk-return (HI/HRR) industries, where the investment environment is often profiled as highly uncertain with high returns, NPV is insufficient to reflect the multidimensional risks, hence unable to capture the extensive investment returns that may consist of non-financial values. This dissertation applies the real option (RO) valuation methodology, supplementing the NPV method to evaluate the return of the sports retail industry (SRI) flagship stores investments. This study further demonstrates that there are strategic values captured by the RO valuation method, complementing the financial values attained by the NPV. To test this assertion, we use case methodology to analyze four flagship investment activities (proprietary business data are concealed). These investments represent various investment options, including growth, expansion, staging, and delay. The cases include projections made prior to the investment, the retrospective application of RO to estimate strategic value, and the actual returns from these investments. Findings demonstrate convincingly RO methodology can and should be usefully applied to supplement the NPV method in HI/HRR industries, and SRI in particular.

In the multifaceted landscape of financial markets, the understanding and application of data science methods are crucial for achieving robustness, fairness, and strategic advancement. This dissertation addresses these critical areas through three interconnected studies. The first study investigates the problem of data imbalance, with particular emphasis on financial applications such as credit risk assessment, where the prevalence of non-defaulting entities overshadows defaulting ones. Traditional classification models often falter under such imbalances, leading to biased predictions. By analyzing linear discriminant functions under conditions where one class's sample size grows indefinitely while the other remains fixed, this study reveals that certain parameters stabilize, providing robust predictions. This robustness ensures model reliability even in skewed data environments. The second study explores anomalies in option pricing, specifically the total positivity of order 2 (TP₂) in call options and the reverse sign rule of order 2 (RR₂) in put options within the S&P 500 index. By examining the empirical significance and occurrence patterns of these violations, the research identifies potential trading opportunities. The findings demonstrate that while these conditions are mostly satisfied, violations can be strategically exploited for consistent positive returns, providing practical insights into profitable trading strategies. The third study addresses the fairness of regulatory stress tests, which are crucial for assessing the capital adequacy of banks. The uniform application of stress test models across diverse banks raises concerns about fairness and accuracy. This study proposes a method to aggregate individual models into a common framework, balancing forecast accuracy and equitable treatment. The research demonstrates that estimating and discarding centered bank fixed effects leads to more reliable and fair stress test outcomes. The conclusions of these studies highlight the importance of understanding the behavior of commonly used models in handling imbalanced data, the strategic exploitation of option pricing anomalies for profitable trading, and the need for fair regulatory practices to ensure financial stability. Together, these findings contribute to a deeper understanding of data science in finance, offering practical insights for regulators, financial institutions, and traders.

Thesis (MBA)--Stellenbosch University, 2005. / ENGLISH ABSTRACT: The oil industry is under pressure to select refinery projects that will provide higher and more predictable returns. In the past Discounted Cash Flow (DCF) techniques have been used to choose between refinery project alternatives. One of the problems with DCF techniques is that they ignore management flexibility when evaluating projects that contain embedded options. Real Option Valuation (ROV) is an approach that takes management flexibility into account and places a value on this flexibility. ROV has been used extensively by the oil industry for the evaluation of oil and gas reserves. The aim of this study is to determine the extent to which the use of ROV will improve the decision making process when evaluating a refining project containing embedded options as well as to determine the most appropriate option valuation method for refining projects. This was done by evaluating a refining project using both a probabilistic DCF approach and the various option pricing models and comparing the results. It was concluded that ROV will improve the decision making process when evaluating refining projects containing embedded options. The most appropriate option pricing method for refining projects was found to be the simulation approach since simulation is already being used by refineries to perform probabilistic DCF analysis. It is not recommended that ROV should be blindly applied to all refining projects containing embedded options. The use of ROV should be limited to larger refining projects for which probabilistic cash flows have been developed and the extent of the ROV analysis required should be determined by a careful review of the net present value (NPV) cumulative probability curves. / AFRIKAANSE OPSOMMING: Die olie industrie is onder druk geplaas om projekte te kies met 'n hoër opbrengs op kapitaal en 'n opbrengs wat meer voorspelbaar is. In die verlede is slegs die Verdiskonteerde Kontant Vloei (VKV) metode gebruik om projekte te selekteer vir die raffinadery. Een van die onderliggende tekortkominge met die gebruik van die VKV metode is dat verskillende bestuursopsies in terme van alternatiewe met ingeboude opsies, nie voldoende ondersoek word nie. Reële Opsie Waardasie (ROW) is 'n metode wat bestuursopsies in ag neem deur 'n waarde te plaas op elke beskikbare bestuursopsie. ROW het wye toepassings in die olie industrie vir die evaluasie van gas en olie reserves. Die doel van hierdie studie is om te bepaal tot watter mate die gebruik van ROW die besluitnemingsproses sal verbeter in terme van die evaluasie van projekte met ingeboude opsies vir raffinaderye en watter opsiewaardasie metode die mees geskikte is vir sulke projekte. 'n Raffinadery projek is evalueer deur beide KV en verskeie opsie-prysbepalingsmetodes te gebruik en die resultate is vergelyk. Die resultate van die studie het bewys dat die ROW metode die besluitnemingsproses verbeter. Die studie het gewys dat die mees geskikte opsie-waardasie metode vir projekte in the raffinadery die simulasie benadering is omdat simulasie alreeds vir probalisties VKV ontleding gebruik word. 'n Verdere aanbeveling is dat die ROW metode nie blindelings gevolg moet word vir alle projekte met ingeboude opsies nie. Die gebruik van ROW moet beperk word tot groter projekte waarvoor probabilistiese kontantvloei alreeds ontwikkel is. Die mate van ROW ontleding moet bepaal word deur 'n noukeurige ondersoek te doen van die kumulatiewe netto huidige waarde-waarskynlikheidskurwe.

Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2007. / The use of options on various stock markets over the world has introduced a unique opportunity for investors to hedge, speculate, create synthetic financial instruments and reduce funding and other costs in their trading strategies. The power of options lies in their versatility. They enable an investor to adapt or adjust her position according to any situation that arises. Another benefit of using options is that they provide leverage. Since options cost less than stock, they provide a high-leverage approach to trading that can significantly limit the overall risk of a trade, or provide additional income. This versatility and leverage, however, come at a price. Options are complex securities and can be extremely risky. In this document several aspects of trading and valuing some exotic options are investigated. The aim is to give insight into their uses and the risks involved in their trading. Two volatility-dependent derivatives, namely compound and chooser options; two path-dependent derivatives, namely barrier and Asian options; and lastly binary options, are discussed in detail. The purpose of this study is to provide a reference that contains both the mathematical derivations and detail in valuating these exotic options, as well as an overview of their applicability and use for students and other interested parties.

Univ., Diss.--Frankfurt/Main, 2004. / Literaturangaben.