M.Comm. / This study is to investigate the derivatives instruments used in other international deregulated electricity markets and how some of these may be used to manage risks incurred in a local Electricity Supply Industry after deregulation. To determine which of the derivatives may be used in the South African market as the most effective hedging instrument. To determine which is most effective will be determined by the contribution to the income of the market participant.

This thesis focuses on the non-arbitrage (fair) pricing of interest rate derivatives, in particular caplets and swaptions using the LIBOR market model (LMM) developed by Brace, Gatarek, and Musiela (1997) and Swap market model (SMM) developed Jamshidan (1997), respectively. Today, in most financial markets, interest rate derivatives are priced using the renowned Black-Scholes formula developed by Black and Scholes (1973). We present new pricing models for caplets and swaptions, which can be implemented in the financial market other than the Black-Scholes model. We theoretically construct these "new market models" and then test their practical aspects. We show that the dynamics of the LMM imply a pricing formula for caplets that has the same structure as the Black-Scholes pricing formula for a caplet that is used by market practitioners. For the SMM we also theoretically construct an arbitrage-free interest rate model that implies a pricing formula for swaptions that has the same structure as the Black-Scholes pricing formula for swaptions. We empirically compare the pricing performance of the LMM against the Black-Scholes for pricing caplets using Monte Carlo methods.

In this thesis the tax treatment of equity option contracts is examined. The writer gives an overview of the derivatives market in general and discusses the nature and effect of equity options in detail. Limited amendments have been made to the South African Income Tax Act No 58 of 1962 ('the Act') since the emergence of derivative instruments and at present only three types of derivative instruments are recognised: forward exchange and option contracts relating to forward exchange, interest rate swaps based on notional capital amounts and option contracts. Other than section 241 of the Act which deems all receipts and accruals from foreign exchange contracts to be income, the other sections dealing with derivatives do not concern themselves with capital or revenue classification. Accordingly, the classification of receipts and accruals arising from an equity option transaction is generally governed by the ordinary principles of South African tax law with the added problem of there being limited South African case law applying these general prinCiples to such transactions. The research undertaken in this thesis results in the establishment of a framework designed to determine the classification as revenue or capital the receipts and accruals arising from equity option contracts. Speculating, trading and investing in equity options is examined with regard to the general principles of South African tax and available case law. Hedging transactions are analysed with specific reference to their exact nature as well as general tax principles and available case law. The analogy of Krugerrands is used to draw parallels with the tax treatment of receipts and accruals arising from equity options used for hedging purposes. Once the theoretical framework has been established for revenue or capital classification, the actual tax treatment of both revenue and capital receipts is examined with reference to the Act and issues such as the gross income definition, the general deduction formula, trading stock and timing provisions are analysed and applied to receipts and accruals arising from equity option transactions. The thesis concludes with a summary of the findings and recommendations are made based on the research conducted.

Firms can use financial derivatives to hedge risks and thereby decrease the probability of bankruptcy and increase total expected tax shields. Firms also can adjust their operational policies in response to fluctuations in prices, a strategy that is often referred to as "operational hedging". In this paper, I investigate the relationship between the optimal financial and operational hedging strategies for a firm, which are endogenously determined together with its capital structure. This allows me to examine how operational hedging affects debt capacity and total expected tax shields and to make quantitative predictions about the relationship between debt issues and hedging policies. I also model the effects of asymmetric information about firms' investment opportunities on their financing and hedging decisions. First, I examine the case in which both debt and hedging contracts are observable. Then, I study the case in which firms' hedging activities are not completely transparent. The models are tested using a data set compiled from the annual reports of North American gold mining companies. Supporting evidence is found for the key predictions of the model under asymmetric information. / Business, Sauder School of / Graduate

Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2006. / An overview of modern and historical interest rate model theory is given with the specific aim of derivative pricing. A variety of stochastic interest rate models are discussed within a South African market context. The various models are compared with respect to characteristics such as mean reversion, positivity of interest rates, the volatility structures they can represent, the yield curve shapes they can represent and weather analytical bond and derivative prices can be found. The distribution of the interest rates implied by some of these models is also found under various measures. The calibration of these models also receives attention with respect to instruments available in the South African market. Problems associated with the calibration of the modern models are also discussed.

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 (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.

Submitted by Elba Lopes (elba.lopes@fecap.br) on 2016-02-04T15:01:00Z No. of bitstreams: 2 Clemil_Robles.pdf: 1063090 bytes, checksum: c8a8fbf9e8a0e811b0f4268c4a413a6d (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-02-04T15:01:00Z (GMT). No. of bitstreams: 2 Clemil_Robles.pdf: 1063090 bytes, checksum: c8a8fbf9e8a0e811b0f4268c4a413a6d (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2003-01-15 / The purpose of this work is to research and compare accounting rules emanated from the FASB and from the Brazilian Central Bank applied to Derivatives. The fact that financial institutions run popular savings funds and the fact that they also represent an important link between several economic agents , enhances the importance of the performance and of the stability of the financial system. The activity of the financial institutions involve several risks which can lead to the insolvency and consequently the ruin of the popular savings. The use of transactions with derivatives by financial institutions as hedging of the operations themselves and for speculation, have become more popular over the years. Therefore it is of utmost importance to know risks those financial institutions run when they carry out said transactions and also how those risks are being dealt with, accounted for and evidenced to their clients. In this work we have tried to compare the accounting rules, apart from evidencing that transactions with derivatives have been carried out according to the international standards. The survey concluded that the Brazilian accounting system derived from the Brazilian Central Bank resembles those of IASB and FASB. Therefore it has been evidenced that those entities outside the scope of the Central Bank, do not possess accounting rules which deal adequately with operations with derivatives. / O prop??sito deste trabalho ?? pesquisar e comparar as normas cont??beis emanadas do FASB (Financial Accounting Standards Board), IASB (International Accounting Standards Board) e do Banco Central do Brasil aplicadas a derivativos. O fato de as institui????es financeiras administrarem recursos da poupan??a popular e de representarem importante elo entre os diversos agentes econ??micos faz com que o desempenho e a estabilidade do sistema financeiro assumam particular relev??ncia, pois a atividade das institui????es financeiras envolve diversos riscos, que podem resultar na sua insolv??ncia e, conseq??entemente, na destrui????o de poupan??a popular. A utiliza????o de opera????es com derivativos pelas institui????es financeiras, que s??o realizadas para fins de hedging das pr??prias opera????es e para especula????o, t??m se acentuado nos ??ltimos anos. Portanto, conhecer os riscos a que essas entidades est??o expostas ao fazerem essas opera????es e como tais riscos est??o sendo gerenciados, contabilizados e evidenciados aos usu??rios ?? de suma import??ncia. Procurou-se no presente trabalho, al??m de comparar as normas cont??beis, efetuar a constata????o de que as opera????es com derivativos das institui????es financeiras brasileiras est??o seguindo o tratamento cont??bil, julgado adequado, pelos principais organismos internacionais normatizadores de regras cont??beis. A pesquisa conclui que o arcabou??o cont??bil brasileiro emanado do Banco Central do Brasil, possui grande similaridade com as normas do IASB e FASB. Por??m, constatou-se que as entidades fora do ??mbito de atua????o do Banco Central n??o possuem normas cont??beis que d??em tratamento adequado ??s opera????es com derivativos.

The objective of this thesis is the implementation of Monte Carlo and quasi-Monte Carlo methods for the valuation of financial derivatives. Advantages and disadvantages of each method are stated based on both the literature and on independent computational experiments by the author. Various methods to generate pseudo-random and quasi-random sequences are implemented in a computationally uniform way to enable objective comparisons. Code is developed in VBA and C++, with the C++ code converted to a COM object to make it callable from Microsoft Excel and Matlab. From the simulated random sequences Brownian motion paths are built using various constructions and variance-reduction techniques including Brownian Bridge and Latin hypercube. The power and efficiency of the methods is compared on four financial securities pricing problems: European options, Asian options, barrier options and mortgage-backed securities. In this paper a detailed step-by-step algorithm is given for each method (construction of pseudo- and quasi-random sequences, Brownian motion paths for some stochastic processes, variance- and dimension- reduction techniques, evaluation of some financial securities using different variance-reduction techniques etc).