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Based on Lyapunov stability theorem, a design methodology of nth order adaptive integral variable structure derivative estimator (AIVSDE) is proposed in this thesis. The proposed derivative estimator not only is an improved version of the existing AIVSDE, but also can be used to estimate the nth differentiation of a smooth signal which has continuous and bounded derivatives up to n+1. A low pass filter is cascaded with AIVSDE so that the effects of noise can be alleviated by adjusting the designing parameters of filter and AIVSDE. The adaptive algorithm is incorporated in the control scheme for removing the a priori knowledge of the upper bound of the observed signal. The stability of the proposed derivative estimator is guaranteed, and the comparison of upper bound of derivative estimation error between recently proposed nonlinear adaptive variable structure derivative estimator (NAVSDE) and AIVSDE is also demonstrated. An example is given for showing the applicability of the proposed AIVSDE.

Field theories with higher derivative gravity duals can violate the viscosity bound. However the extent of the violation is not arbitrary since it depends on the coupling of the higher derivative interactions, which can be constrained by requiring consistency of the boundary field theory. In particular, in Einstein-Gauss-Bonnet (EGB) gravity, the coupling λ can be constrained by requiring that the dual theory respect causality. We investigate the upper bound on λ by computing the quasinormal modes of an EGB black hole in order to explicitly find and interpret the causality violating excitations. We find that in the limit of infinite spatial momentum the imaginary part of these modes approaches 0, while the phase velocity approaches 1 from above. This behaviour at high momentum is confirmed by the existence of a lightlike pole in the stress-energy tensor two-point function. We therefore confirm that the requirements to interpret the poles of the two-point function as causality violating, propagating modes are met in the limit of infinite spatial momentum. The presence of such excitations not only constrains the viscosity bound but also limits the allowed couplings of EGB gravity. / Graduate / 0798 / 0753 / mharder@uvic.ca

This thesis examines finite dimensional representability of Forward Rate and LIBOR models. A new approach is examined. This approach is more general, elementary, and relevant to finance when compared with existing approaches. This new approach is applied to the following infinite dimensional equations used in finance: ?Gaussian Heath, Jarrow and Morton model; ?Free 1 Heath, Jarrow and Morton model; ?Brace, G?atarek and Musiela???s LIBOR model. Stronger results have been achieved using this approach. The results are as follows: ?The Gaussian HJM model can be represented in finite dimensions if and only if the volatility satisfies a particular differential equation. In which case the finite dimensional representation can be explicitly written; ?The Brace, G?atarek and Musiela???s LIBOR model with one dimensional Wiener process cannot be represented in finite dimensions (other than in a trivial case); ?The Brace, G?atarek and Musiela???s LIBOR model with multidimen-sional Wiener process, and Free HJM have a finite dimensional repre-sentation only if the initial yield curves satisfy a restrictive differential equation. This thesis is arranged as follows ?Chapter 1 is an introduction to this thesis and derivative pricing in general. The reader is referred to section 1.4 titled ???This Thesis?for a more detailed description of the approach of this thesis and its results. ?Chapter 2 contains a brief summary of results from the theory of stochastic processes, stochastic calculus and stochastic equations in infinite dimensions ?Chapter 3 contains an overview of spot market pricing models including the Cox, Ross and Rubinstein and Black and Scholes models. ?Chapter 4 contains an overview of the fixed income market pricing models including the Heath, Jarrow and Morton model; Musiela???s re-formulation of the HJM model; the Goldys, Musiela and Sondermann model; and the Brace, G?atarek and Musiela LIBOR model. ?Chapter 5 contains the primary results of this thesis. Finite Dimen-sional Representability is defined formally and applied to the Musiela reformulated Gaussian HJM model; Musiela reformulated free HJM model; and the Brace, G?atarek and Musiela LIBOR model. This ap-proach and results are compared with the literature.

Thesis (M.S.) -- Worcester Polytechnic Institute. / Keywords: security; derivatives; forward; measure; binomial tree. Includes bibliographical references (p.34-35).

Thesis (M.Sc.)--York University, 2006. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 92-94). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR29633

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Credit Default Swap; Hazard rate approach; Merton model; Credit Risk. Includes bibliographical references (p. 46-48).

The lack of specific tax legislation and practice dealing with the taxation of derivatives in South Africa necessitates the construction of a framework for the taxation of derivatives: the subject of this dissertation. The lack of sophistication within the Income Tax Act, No. 58 of 1962 and the lack of clarity provided by the South African Revenue Service with regard to derivatives, specifically in a hedging context, is expected to be overcome to a large degree by virtue of the contents of this dissertation. The dissertation considers the meaning of a derivative and a hedge in a tax context and culminates in the drafting of suggested definitions of a derivative and a hedge to be housed within our tax legislation. The definitions have been constructed from key themes and features extracted from various comparative studies. Given the changes in accounting methodologies and practice of derivative transactions, it is considered that the need, from a tax perspective, is to move closer to the accounting treatment of gains and losses on derivative transactions. The analysis in this dissertation favours this approach in the instance specifically where derivatives are transacted as a hedge of an underlying capital transaction. The purposes for which derivatives are used are finally considered specifically in the context of the common law doctrine of substance over form. The subjective test of the taxpayer’s mindset plays a major part in balancing the legal form of a transaction and its legal substance. It is hoped that a fresh view on the taxation of derivatives and the construction of this framework provides users of tax legislation with a concise pathway to the tax effect and consequences of their application. / Prof. D Coetsee

In 1985, Merrill Lynch introduced Liquid Yield Option Notes, or LYONS into the exotic derivative corporate capital market. Based on a plain vanilla bond, its features were changed to accommodate risk protection for issuers and holders. The hybrid bond is both callable and puttable, it is convertible into common stock, and issued as a zero coupon discount bond. The put and call options are intended to reduce short-term interest rate risk corporations and holders are exposed to. Smith and Smithson (1990) propose that LYONs were introduced to reduce underinvestment, asset substitution, and claim dilution. If LYONs were designed to reduce agency costs and align stockholder/bondholder interests several factors can be associated with these securities according to Nash {1994). Identifying firms likely to issue these securities can be found by examining several financial ratios including, debt to equity, leverage, standard deviation of earnings, and debt rating. It is important to know what type of firm is issuing these securities and if stated objectives align with the empirical evidence embedded in the contractual elements. Few studies have been done in the areas of exotic derivative options but as the amount of capital raised through LYONs approaches $50 billion, it is important for investors to become familiar with this instrument, as many institutional investors for pension funds, and other mutual accounts buy into these instruments. Updating the work of Nash (1994) to include issues of LYONs after 1993 to present will test the indicators defined by his contracting-cost explanation for the existence of LYONs. Further knowledge can be gained by assessing more recent issues. Analyzing how recent interest rate, and federal government regulation of the exotic derivative securities market provides insight into future derived offerings and objectives. This thesis will describe the environment and provide insight into the motivations for bond issuers and holders. My intent is to make an assumption about the outcome versus stated objectives. With a sample set of 20 contracts randomly selected from years 1985-2002, I examine several variables within the contracts and the corporations issuing them. Factors such as yield, maturity, face value, conversion premium, and industry are used to analyze the contracts. Factors such as debt to equity, leverage, standard deviation of earnings, are used to determine a correlation in the likelihood of issuing LYONs. Trading history is examined to determine which risk is best protected against by the attached put and call options, and whether corporations or investors are typically realizing the benefits.

Thesis (M.B.A.)--University of Hong Kong, 1998. / Includes bibliographical references (leaf 40-41).