Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 114-116). Also available on the Internet.

Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2009. / In this thesis, we investigate two numerical methods to price nancial options. We look at two types of options, namely European options and Asian options. The numerical methods we use are the nite di erence method and numerical inversion of the Laplace transform. We apply nite di erence methods to partial di erential equations with both uniform and non-uniform spatial grids. The Laplace inversion method we use is due to Talbot. It is based on the midpoint-type approximation of the Bromwich integral on a deformed contour. When applied to Asian options, we have the problem of computing the hypergeometric function of the rst kind. We propose a new method for numerically calculating the hypergeometric function. This method too is based on using Talbot contours. Throughout the thesis, we use the Black-Scholes equation as our benchmark problem.

The feasibility of capital projects in an uncertain world can be determined in several ways. One of these methods is real options valuation which arose from financial option valuation theory. On the other hand fuzzy set theory was developed as a mathematical framework to capture uncertainty in project management. The valuation of real options using fuzzy numbers represents an important refinement to determining capital projects' feasibility using the real options approach. The aim of this study is to determine whether the deferral of the decommissioning time (by a decade) of an electricity-generating nuclear plant in South Africa increases decommissioning costs. Using the fuzzy binomial approach, decommissioning costs increase when decommissioning is postponed by a decade whereas use of the fuzzy Black-Scholes approach yields the opposite result. A python code was developed to assist in the computation of fuzzy binomial trees required in our study and the results of the program are incorporated in this thesis. / KMBT_363 / Adobe Acrobat 9.54 Paper Capture Plug-in

American options are the most commonly traded financial derivatives in the market. Pricing these options fairly, so as to avoid arbitrage, is of paramount importance. Closed form solutions for American put options cannot be utilised in practice and so numerical techniques are employed. This thesis looks at the work done by other researchers to find an analytic solution to the American put option pricing problem and suggests a practical method, that uses Monte Carlo simulation, to approximate the American put option price. The theory behind option pricing is first discussed using a discrete model. Once the concepts of arbitrage-free pricing and hedging have been dealt with, this model is extended to a continuous-time setting. Martingale theory is introduced to put the option pricing theory in a more formal framework. The construction of a hedging portfolio is discussed in detail and it is shown how financial derivatives are priced according to a unique riskneutral probability measure. Black-Scholes model is discussed and utilised to find closed form solutions to European style options. American options are discussed in detail and it is shown that under certain conditions, American style options can be solved according to closed form solutions. Various numerical techniques are presented to approximate the true American put option price. Chief among these methods is the Richardson extrapolation on a sequence of Bermudan options method that was developed by Geske and Johnson. This model is extended to a Repeated-Richardson extrapolation technique. Finally, a Monte Carlo simulation is used to approximate Bermudan put options. These values are then extrapolated to approximate the price of an American put option. The use of extrapolation techniques was hampered by the presence of non-uniform convergence of the Bermudan put option sequence. When convergence was uniform, the approximations were accurate up to a few cents difference.

This study has a twofold purpose: to demonstrate the use of the Marquardt compromise method in estimating the unknown parameters contained in the probability call-option pricing models and to test empirically the following models: the Boness, the Black-Scholes, the Merton proportional dividend, the Ingersoll differential tax, and the Ingersoll proportional dividend and differential tax.

Orientador: Jose Mario Martinez / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T04:59:49Z (GMT). No. of bitstreams: 1 Prudente_LeandrodaFonseca_M.pdf: 2877541 bytes, checksum: c2a57346fe1ba93469b385a71de6c2da (MD5) Previous issue date: 2009 / Resumo: Nesta dissertação expomos algumas propriedades das opções e desenvolvemos a teoria clássica que resulta na Equação de Black-Scholes Generalizada, o modelo utilizado no mercado para precificar uma opção. Neste cenário apresentamos o Princípio da Retrodifusão. A ideia de obtermos a Equação de Black-Scholes por meios mais simples e que possibilitem uma interpretação intuitiva desta equação. Mostramos uma maneira numérica para resolver a Equação de Black-Scholes Generalizada e por fim desenvolvemos um método para estimar a superfície de volatilidade de um ativo usando como ferramenta conhecidas opções comercializadas. / Abstract: In this work expose some properties of the options and developed the classical theory which results in the Generalized Black-Scholes equation, the model used in the market for pricing an option. In this context we present the Princípio da Retrodifusão. The idea is to get the Black-Scholes equation by simpler means and enabling an intuitive interpretation of this equation. We show a numerical way to solve the Generalized Black-Scholes equation and finally developed a method to estimate the volatility surface of an asset using as a tool known options traded. / Mestrado / Mestre em Matemática Aplicada

M.Sc.

This document demonstrates the use of the C++ programming language as a simulation tool in the efficient pricing of exotic European options. Extensions to the basic problem of simulation pricing are undertaken including variance reduction by conditional expectation, control and antithetic variates. Ultimately we were able to produce a modularized, easily extend-able program which effectively makes use of Monte Carlo simulation techniques to price lookback, Asian and barrier exotic options. Theories of variance reduction were validated except in cases where we used control variates in combination with the other variance reduction techniques in which case we observed increased variance. Again, the main aim of this half thesis was to produce a C++ program which would produce stable pricings of exotic options.

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.

This study develops a real options model of agbiotechnology and is applied to three genetically modified (GM) traits. Each trait is evaluated as growth options where technical or marketing milestones must be completed before management can exercise the option to invest further in trait development. The real options values are evaluated by employing a binomial tree which is simulated using distributions for random elements within stages of the growth option. Mean option values were negative for the discovery stage for fusarium-resistant wheat and for all but the regulatory submission stage for Roundup Ready wheat. The length of the regulatory submission stage had the greatest negative impact on the value of the option while the ability of the firm to maximize technology-use-fees had the greatest positive impact. Additionally, traits adapted to crops with larger potential market size are more likely to be in the money than traits developed for smaller market segments.