The aim of this thesis is to estimate the volatility function of continuoustime stochastic models. The estimation of the volatility of the following wellknown international stock market indexes is presented as an application: Dow Jones Industrial Average, Standard and Poor’s 500, NIKKEI 225, CAC 40, DAX 30, FTSE 100 and IBEX 35. This estimation is studied from two different perspectives: a) assuming that the volatility of the stock market indexes displays shortrange dependence (SRD), and b) extending the previous model for processes with longrange dependence (LRD), intermediaterange dependence (IRD) or SRD. Under the efficient market hypothesis (EMH), the compatibility of the Vasicek, the CIR, the Anh and Gao, and the CKLS models with the stock market indexes is being tested. Nonparametric techniques are presented to test the affinity of these parametric volatility functions with the volatility observed from the data. Under the assumption of possible statistical patterns in the volatility process, a new estimation procedure based on the Whittle estimation is proposed. This procedure is theoretically and empirically proven. In addition, its application to the stock market indexes provides interesting results.

The objective of the research reported in this dissertation is to conduct an empirical test of the hypothesis that, excluding income tax effects, the cost of capital to a firm is independent of the degree of financial leverage employed by the firm. This hypothesis, set forth by Franco Modigliani and Merton Miller in 1958, represents a challenge to the traditional view on the subject, a challenge which carries implications of considerable importance in the field of finance. The challenge has led to a lengthy controversy which can ultimately be resolved only by subjecting the hypothesis to empirical test. The basis of the test was Modigliani and Miller's Proposition II, a corollary of their fundamental hypothesis. Proposition II, in effect, states that equity investors fully discount any increase in risk due to financial leverage so that there is no possibility for the firm to reduce its cost of capital by employing financial leverage. The results of the research reported in this dissertation do not support that contention. The study indicates that, if equity investors require any increase in premium for increasing financial leverage, the premium required is significantly less than that predicted by the Modigliani-Miller Proposition II, over the range of debt-equity ratios covered by this study. The conclusion, then, is that it is possible for a firm to reduce its cost of capital by employing financial leverage. A secondary conclusion that can be drawn from this study is that earning power is an important variable to consider for inclusion in a regression model intended for use in investigating the effect of financial leverage on the cost of capital. The estimated partial regression coefficient of the earning-power variable was negative and highly significant in every cross-section year. Furthermore, earning power showed strong negative partial correlation with the debt-equity ratio. Therefore, omission of the earning-power variable from the regression model would have introduced upward bias into the estimated regression coefficient of the debt-equity ratio, making it appear that investors were reacting adversely to increasing debt-equity ratio. However, models used in previous tests of the Modigliani-Miller hypothesis have not included earning power.

In this thesis we investigate the application of two heuristic methods, genetic algorithms and tabu/scatter search, to the optimisation of realistic portfolios. The model is based on the classical mean-variance approach, but enhanced with floor and ceiling constraints, cardinality constraints and nonlinear transaction costs which include a substantial illiquidity premium, and is then applied to a large I 00-stock portfolio. It is shown that genetic algorithms can optimise such portfolios effectively and within reasonable times, without extensive tailoring or fine-tuning of the algorithm. This approach is also flexible in not relying on any assumed or restrictive properties of the model and can easily cope with extensive modifications such as the addition of complex new constraints, discontinuous variables and changes in the objective function. The results indicate that that both floor and ceiling constraints have a substantial negative impact on portfolio performance and their necessity should be examined critically relative to their associated administration and monitoring costs. Another insight is that nonlinear transaction costs which are comparable in magnitude to forecast returns will tend to diversify portfolios; the effect of these costs on portfolio risk is, however, ambiguous, depending on the degree of diversification required for cost reduction. Generally, the number of assets in a portfolio invariably increases as a result of constraints, costs and their combination. The implementation of cardinality constraints is essential for finding the bestperforming portfolio. The ability of the heuristic method to deal with cardinality constraints is one of its most powerful features. / Decision Sciences / M. Sc. (Operations Research)

Bibliografia: p. 46-48 / Dissertação (mestrado) - Faculdade de Economia e Finanças Ibmec, Rio de Janeiro, 2014. / Devido à crescente importância dos mercados financeiros nas últimas décadas, o risco de crédito tem se tornado um tema fundamental na tomada de decisões acerca de investimentos, taxas de financiamento, solvência corporativa, tendência e perspectivas etc. Os modelos de avaliação de risco de crédito, em geral, podem ser classificados em duas categorias: quantitativo e qualitativo. Modelos quantitativos buscam analisar informações de demonstrativos financeiros e seus indicadores, enquanto modelos qualitativos focam na análise de variáveis intangíveis que afetam os negócios globais. Estes modelos normalmente seguem uma estrutura "top-down" de análise setorial, competitividade e comparação de pares e gestão. O objetivo desta dissertação é apresentar um modelo de classificação de risco setorial com base em métodos de análise multicritério que possam mensurar a importância das variáveis que afetam os setores da economia brasileira, bem como a influência entre estas. O modelo é baseado, principalmente, no método Weighted Influence Non-Linear Gauge System. Acerca dos julgamentos sobre as variáveis, o modelo baseia-se na utilização do método Analytic Hierarchy Process. O resultado do modelo é apresentado através de níveis de risco, aplicado a quatorze setores da economia brasileira. A dissertação se encerra com uma discussão sobre os resultados, bem como com um esboço do direcionamento para futuras pesquisas. / Due to the increasing importance of the financial market over the past decades, credit risk has become a paramount issue in investment, loan spreads, corporate solvency, trends and prospetcs, etc. Credit risk evaluation models may be classified in two broad categories: quantitative and qualitative. Quantitative models seek to analyze information from financial statement and indexes, while qualitative models focus on the analysis of intangible variables that affect global business. These models typically follow a top-down approach by analyzing the industry risk, competitiveness and peer comparison and management. The aim of this thesis is to present an industry risk assessment model based on multicriteria analysis methods that can measure the strengh of variables that affect the industries of Brazilian economy, as well as the influence between them. The model is based primarily on the Weighted Influence Non-Linear Gauge System method. Concerning human judgements about the variables, the model is founded on the use of the Analytic Hierarchy Process method. The result from the model is presented through risk levels, applied to fourteen industries in the Brazilian economy. The thesis closes with a discussion of results, as well as with an outline to future research directions.

Thesis (M.Sc. (Applied Mathematics)) -- University of Limpopo, 2019 / Functional Itˆo calculus is based on an extension of the classical Itˆo calculus to functionals depending on the entire past evolution of the underlying paths and not only on its current value. The calculus builds on F¨ollmer’s deterministic proof of the Itˆo formula Föllmer (1981) and a notion of pathwise functional derivative recently proposed by Dupire (2019). There are no smoothness assumptions required on the functionals, however, they are required to possess certain directional derivatives which may be computed pathwise, see Cont and Fournié (2013); Schied and Voloshchenko (2016a); Cont (2012). In this project we revise the functional Itô calculus together with the notion of quadratic variation. We compute the pathwise change of variable formula utilizing the functional Itô calculus and the quadratic variation notion. We study the martingale representation for the case of weak derivatives, we allow the vertical operator, rX, to operate on continuous functionals on the space of square-integrable Ft-martingales with zero initial value. We approximate the hedging strategy, H, for the case of path-dependent functionals, with Lipschitz continuous coefficients. We study some hedging strategies on the class of discounted market models satisfying the quadratic variation and the non-degeneracy properties. In the classical case of the Black-Scholes, Greeks are an important part of risk-management so we compute Greeks of the price given by path-dependent functionals. Lastly we show that they relate to the classical case in the form of examples. / NRF and AIMS-SA

Nicotinic acid adenine dinucleotide phosphate (NAADP) is a potent Ca²⁺ mobilising messenger in mammalian and non-mammalian cells. Studies on a variety of cell types suggest that NAADP evokes Ca²⁺ release from a lysosome-related store and via activation of a receptor distinct from either ryanodine receptors (RyR) or inositol 1,4,5-trisphosphate (IP₃) receptors (IP₃R). However, the identity of the NAADP receptor has, until now, remained elusive. In this thesis I have shown that NAADP-evoked Ca²⁺ release from lysosomes is underpinned by two-pore channels (TPCs), of which there are 3 subtypes, TPC1, TPC2 and TPC3. When stably over-expressed in HEK293 cells, TPC2 was found to be specifically targeted to lysosomes, while TPC1 and TPC3 were targeted to endosomes. Initial Ca²⁺ signals via TPC2, but not those via TPC1, were amplified into global Ca²⁺ waves by Ca²⁺-induced Ca²⁺ release (CICR) from the endoplasmic reticulum (ER) via IP₃Rs. I have shown that, consistent with a role for TPCs in NAADP-mediated Ca²⁺ release, TPC2 is expressed in pulmonary arterial smooth muscle cells (PASMCs), is likely targeted to lysosomal membranes, and that TPCs also underpin NAADP-evoked Ca²⁺ signalling in this cell type. However, and in contrast to HEK293 cells, in PASMCs NAADP evokes spatially restricted Ca²⁺ bursts that are amplified into global Ca²⁺ waves by CICR from the sarcoplasmic reticulum (SR) via a subpopulation of RyRs, but not via IP₃Rs. I have demonstrated that lysosomes preferentially co-localise with RyR subtype 3 (RyR3) in the perinuclear region of PASMCs to comprise a “trigger zone” for Ca²⁺ signalling by NAADP, away from which a propagating Ca²⁺ wave may be carried by subsequent recruitment of RyR2. The identification of TPCs as a family of NAADP receptors may further our understanding of the mechanisms that confer the versatility of Ca²⁺ signalling which is required to regulate such diverse cellular functions as gene expression, fertilization, cell growth, and ultimately cell death.

published_or_final_version / Business Administration / Master / Master of Business Administration

This thesis presents several problems based on papers written jointly by the author and Dr. Christian-Oliver Ewald. Firstly, the author extends the model presented by Fershtman and Nitzan (1991), which studies a deterministic differential public good game. Two types of volatility are considered. In the first case the volatility of the diffusion term is dependent on the current level of public good, while in the second case the volatility is dependent on the current rate of public good provision by the agents. The result in the latter case is qualitatively different from the first one. These results are discussed in detail, along with numerical examples. Secondly, two existing lines of research in game theoretic studies of fisheries are combined and extended. The first line of research is the inclusion of the aspect of predation and the consideration of multi-species fisheries within classical game theoretic fishery models. The second line of research includes continuous time and uncertainty. This thesis considers a two species fishery game and compares the results of this with several cases. Thirdly, a model of a fishery is developed in which the dynamic of the unharvested fish population is given by the stochastic logistic growth equation and it is assumed that the fishery harvests the fish population following a constant effort strategy. Explicit formulas for optimal fishing effort are derived in problems considered and the effects of uncertainty, risk aversion and mean reversion speed on fishing efforts are investigated. Fourthly, a Dixit and Pindyck type irreversible investment problem in continuous time is solved, using the assumption that the project value follows a Cox-Ingersoll- Ross process. This solution differs from the two classical cases of geometric Brownian motion and geometric mean reversion and these differences are examined. The aim is to find the optimal stopping time, which can be applied to the problem of extracting resources.

by Wong Man Kit, Andy, Yu Miu Ki. / Thesis (M.B.A.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 53-54). / ABSTRACT --- p.ii / ACKNOWLEDGEMENT --- p.iii / TABLE OF CONTENTS --- p.iv / Chapter / Chapter I. --- INTRODUCTION --- p.1 / Credit Risk --- p.2 / Operational risk --- p.3 / Liquidity risk --- p.3 / Legal risk --- p.3 / Market Risk --- p.3 / Model risk --- p.4 / Chapter II. --- LITERATURE REVIEW --- p.5 / Value at Risk (VaR) --- p.5 / Minimum Variance --- p.7 / Dollar equivalence --- p.8 / Statistical Hedging --- p.8 / Risk and Return in an Imperfect Hedge --- p.8 / Expected return and standard deviation in a hedged position --- p.9 / Risk and Return in an actual hedge --- p.11 / Optimal Hedge Ratio --- p.13 / Deriving Optimal Hedge Ratio h* --- p.15 / Computing the minimum risk hedge ratio by regression --- p.16 / Basis Risk --- p.18 / Sources of Basis Risk --- p.19 / Variation in the equilibrium price relationship between cash and futures --- p.19 / "Random ""noise"" in the price process" --- p.19 / Mismatch between cash position and the underlying for the future --- p.20 / Hedging Effectiveness --- p.21 / Chapter III. --- DATA AND METHODOLOGY --- p.25 / Data --- p.25 / Data Collection --- p.25 / Data Selection --- p.25 / Data Manipulation --- p.26 / Methodology --- p.27 / Part I: The Selection of the Portfolios --- p.27 / Part II: The Determination of the Hedge Ratio --- p.28 / Part III: Hedged vs. Unhedged --- p.29 / Part IV: Data Analysis & Comparison --- p.31 / Chapter IV. --- FINDINGS --- p.35 / High volatility of Hong Kong market --- p.35 / Manipulation of institutional investors --- p.36 / Hong Kong financial market are less mature --- p.36 / Less efficient information flow --- p.37 / Less Sophisticated Investors --- p.38 / Results and Discussion --- p.39 / Empirical Results --- p.40 / Explanation for the differences --- p.42 / Limitations --- p.47 / Learning Period --- p.47 / Cross Hedging --- p.47 / Mismatch between the futures and the underlying index --- p.48 / Missing Stock Data in the S&P500 --- p.49 / Chapter V. --- CONCLUSION --- p.50 / Tradeoff between risk and return --- p.50 / Hedge Effectiveness --- p.51 / BIBLIOGRAPHY --- p.53

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