This thesis studies binomial and trinomial lattice approximations in Black-Scholes type option pricing models. Also, it covers the basics of these models, derivations of model parameters by several methods under different kinds of distributions. Furthermore, the convergence of binomial model to normal distribution, Geometric Brownian Motion and Black-Scholes model isdiscussed. Finally, the connections and interrelations between discrete random variables under the Lattice approach and continuous random variables under models which follow Geometric Brownian Motion are discussed, compared and contrasted.

M.Com. (Economics) / Please refer to full text to view abstract

M.Com. (Econometrics) / The main purpose of this study is the combining of forecasts with special reference to major macroeconomic series of South Africa. The study is based on econometric principles and makes use of three macro-economic variables, forecasted with four forecasting techniques. The macroeconomic variables which have been selected are the consumer price index, consumer expenditure on durable and semi-durable products and real M3 money supply. Forecasts of these variables have been generated by applying the Box-Jenkins ARIMA technique, Holt's two parameter exponential smoothing, the regression approach and mUltiplicative decomposition. Subsequently, the results of each individual forecast are combined in order to determine if forecasting errors can be minimized. Traditionally, forecasting involves the identification and application of the best forecasting model. However, in the search for this unique model, it often happens that some important independent information contained in one of the other models, is discarded. To prevent this from happening, researchers have investigated the idea of combining forecasts. A number of researchers used the results from different techniques as inputs into the combination of forecasts. In spite of the differences in their conclusions, three basic principles have been identified in the combination of forecasts, namely: i The considered forecasts should represent the widest range of forecasting techniques possible. Inferior forecasts should be identified. Predictable errors should be modelled and incorporated into a new forecast series. Finally, a method of combining the selected forecasts needs to be chosen. The best way of selecting a m ethod is probably by experimenting to find the best fit over the historical data. Having generated individual forecasts, these are combined by considering the specifications of the three combination methods. The first combination method is the combination of forecasts via weighted averages. The use of weighted averages to combine forecasts allows consideration of the relative accuracy of the individual methods and of the covariances of forecast errors among the methods. Secondly, the combination of exponential smoothing and Box-Jenkins is considered. Past errors of each of the original forecasts are used to determine the weights to attach to the two original forecasts in forming the combined forecasts. Finally, the regression approach is used to combine individual forecasts. Granger en Ramanathan (1984) have shown that weights can be obtained by regressing actual values of the variables of interest on the individual forecasts, without including a constant and with the restriction that weights add up to one. The performance of combination relative to the individual forecasts have been tested, given that the efficiency criterion is the minimization of the mean square errors. The results of both the individual and the combined forecasting methods are acceptable. Although some of the methods prove to be more accurate than others, the conclusion can be made that reliable forecasts are generated by individual and combined forecasting methods. It is up to the researcher to decide whether he wants to use an individual or combined method since the difference, if any, in the root mean square percentage errors (RMSPE) are insignificantly small.

D.Com. (Econometrics) / The main aim with the thesis was to outline the use of regional econometric modelling as a technique for the modelling of the interdependency in the development regions of South Africa. In particular, an regional econometric model of Region H was constructed. There is no doubt that modelling is here to stay - as part of the analytical process used in scholarly studies and in applications, especially for making policy in both the public and privatedomain. Although macro-econometric modelling has been withus for sometime, the art of building large-scale· regional economic models is relatively new, especially in South Africa where such models have never been in use. The problem of forecasting regional economic activity has become an important component of regional research. The most frequently used forecasting techniques have been input-output model. A regional econometric model can be defined as a set of equations, sometimes highly simultaneous, describing the economic structure of a regional economy. The parameters of the equations are estimated economically largely by regression equations.

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Ni, Rui = 關于Kolmogorov常數以及湍流熱對流中能量耗散率、加速度統計、環流反轉研究 / 倪睿. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 105-119). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Ni, Rui = Guan yu Kolmogorov chang shu yi ji tuan liu re dui liu zhong neng liang hao san lu, jia su du tong ji, huan liu fan zhuan yan jiu / Ni Rui.

by Cheung Kei Wai. / Parallel title in Chinese. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 119-123). / Acknowledgement --- p.ii / Abstract --- p.iii / List of Abbreviations --- p.vii / List of Figure and Table Captions --- p.viii / List of Publication --- p.xiii / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Normal Diffusion --- p.4 / Chapter 1.2 --- Statistical Origin of Anomalous Diffusion --- p.10 / Chapter 1.3 --- Various Models of Diffusion --- p.15 / Chapter 2. --- Scaling Theory of Hopping Transport in One Dimension --- p.21 / Chapter 2.1 --- "Scaling Exponents, the Models and their Solutions" --- p.22 / Chapter 2.2 --- Numerical Simulations --- p.32 / Chapter 2.3 --- Relations to Diffusion on Fractals and Hierarchical Structures --- p.37 / Chapter 2.4 --- Non-Markovian Nature of Results and Quasi-localization Effect --- p.42 / Chapter 3. --- Renormalization Group (RG) Analysis of the Problem --- p.43 / Chapter 3.1 --- The Length Scale Renormalization (LSR) --- p.45 / Chapter 3.2 --- Application of the LSR to Random Barrier Model --- p.52 / Chapter 3.2.1 --- The distribution of the renormalized coupling constants / Chapter 3.2.2 --- Behaviour of W and V under the LSR transformation / Chapter 3.3.3 --- The scaling exponents from LSR / Chapter 3.3 --- Scaling Form of Diffusion Front --- p.66 / Chapter 4. --- Diffusion in Hierarchical Systems --- p.72 / Chapter 4.1 --- Scaling and Probability Densities --- p.75 / Chapter 4.2 --- Exact Renormalization and Lattice Green Function --- p.82 / Chapter 4.3 --- The Range of Diffusion --- p.89 / Chapter 5. --- Biased Diffusion --- p.95 / Chapter 5.1 --- Scaling Theory --- p.98 / Chapter 5.1.1 --- Linear Response / Chapter 5.1.2 --- Diffusion-Drift Crossover / Chapter 5.2 --- Crossover Behaviour under an Additional Bias --- p.103 / Chapter 6. --- Physical Realizations and Related Problems --- p.108 / Chapter 6.1 --- Physical Realizations --- p.109 / Chapter 6.2 --- Equivalence with Random Resistor Network (RRN) Problems --- p.113 / Chapter 7. --- Discussion and Conclusion --- p.116 / References --- p.119 / Chapter Appendix A --- Derivation of Eq. (1.3.8) --- p.124 / Chapter Appendix B --- Derivation of Eq. (1.3.10) --- p.126 / Chapter Appendix C --- Sampling from a Distribution --- p.129 / Chapter Appendix D --- Scaling Form of P (s) in Ordered System --- p.130 / Chapter Appendix E --- Explicit Form of the Lattice Green Function --- p.132

by Leung Ping Ngok. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 39). / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.iii / LIST OF ILLUSTRATIONS --- p.v / Chapter / Chapter I. --- INTRODUCTION --- p.1 / Chapter II. --- THE MODEL --- p.11 / Chapter III. --- THE ANALYSIS --- p.16 / Case 1 - Tariff t --- p.16 / Case 2 - Quota --- p.19 / Chapter i. --- The license is distributed among the two countries by a ratio λ whereas 0< λ<1 --- p.19 / Chapter ii. --- The license is distributed among the internal organizations --- p.28 / Chapter IV. --- DISCUSSION AND CONCLUSION --- p.34 / BIBLIOGRAPHY --- p.39

by Siu-Keung Wan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 69-70). / Chapter Chapter 1 --- Introduction and Review / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Review --- p.3 / Chapter Chapter 2 --- A general IRR model for a system with unobservable states / Chapter 2.1 --- Model and assumptions --- p.8 / Chapter 2.2 --- Long-run average cost per unit time incurred in a replacement cycle --- p.14 / Chapter Chapter 3 --- The Algorithm / Chapter 3.1 --- The key point and the local turning point of the average cost --- p.16 / Chapter 3.2 --- A finite algorithm --- p.23 / Chapter Chapter 4 --- Numerical examples and sensitivity analysis with discussion / Chapter 4.1 --- Weibull Distribution Case --- p.25 / Chapter 4.2 --- Gamma Distribution Case --- p.28 / Chapter 4.3 --- Exponential Distribution Case --- p.30 / Chapter 4.4 --- Sensitivity analysis --- p.32 / Chapter 4.5 --- Conclusion and further development --- p.38 / Figures --- p.40 / Tables --- p.46 / References --- p.69

Lam Fong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 67-68). / Abstracts in English and Chinese. / Chapter 1 --- Background --- p.1 / Chapter 1.1 --- Bond and Yield --- p.1 / Chapter 1.1.1 --- Bond [8] --- p.1 / Chapter 1.1.2 --- Yields --- p.3 / Chapter 1.1.3 --- Qualitative Nature of Price-Yield Curves --- p.5 / Chapter 1.2 --- "Duration, Convexity and Time Value" --- p.8 / Chapter 1.2.1 --- Duration --- p.8 / Chapter 1.2.2 --- Qualitative Properties of Duration --- p.10 / Chapter 1.2.3 --- Convexity --- p.16 / Chapter 1.2.4 --- Literatures Review of Duration and Convexity --- p.17 / Chapter 1.2.5 --- Time Value --- p.20 / Chapter 2 --- Management of Interest Rate Risk --- p.22 / Chapter 2.1 --- Laddered Strategy --- p.23 / Chapter 2.2 --- Dumbbell Strategy --- p.24 / Chapter 2.3 --- Immunization Strategy --- p.25 / Chapter 2.4 --- Consideration of Convexity for Managing Interest Rate Risk --- p.26 / Chapter 2.5 --- Duration Targeting[l2] --- p.28 / Chapter 2.6 --- Immunizing Default-Free Bond Portfolios with a Duration Vec- tor [2] --- p.29 / Chapter 2.7 --- The need of Dynamic Global Portfolio Immunization Theorem --- p.32 / Chapter 3 --- Multi-Period Portfolio Selection --- p.34 / Chapter 3.1 --- Objective --- p.34 / Chapter 3.2 --- Dynamic Programming Formulation --- p.35 / Chapter 3.3 --- Specific Situation --- p.46 / Chapter 3.4 --- Summary of Implementation Results --- p.59 / Chapter 4 --- Summary --- p.64 / Bibliography --- p.67 / A Matlab Program of the Dynamic Portfolio Selection --- p.69