by Leung Kwong Tak. / Bibligraphy: leaves 185-192 / Thesis (M.Phil.) -- Chinese University of Hong Kong, 1982

本論文包含兩個部份。第一個部份討論怎樣用不變方差彈性 (CEV)隨機過程的擬有界 (quasi-bounded)特性去描述擁有目標區特色 (target zone feature)貨幣的動態。利用最大相似估計法 (maximum likelihood estimation)，我們能夠決定不變方差彈性隨機過程是否能為港元聯繫匯率制度給予一個有效描述。這個資訊能給予我們對聯繫匯率制度有更好的理解和一些其他用途，例如為擁有目標區特色的貨幣期權定價。第二個部份會討論利用相似變換 (similarity transformations)找出擁有雙面界限和不變方差彈性隨機過程的相關金融資產的首次穿越時間分佈 (first-passage-time distribution)。首次穿越時間分佈在計量金融上擁有廣泛應用，例如很多路徑相關奇異期權 (exotic options of path dependent nature)問題便和首次穿越時間分佈有密切關係。 / This thesis consists of two parts. The first part discusses how CEV processes can be used as a quasi-bounded process to describe the dynamics of the target zone feature of a currency. By means of the maximum likelihood estimation (MLE), we are able to determine if the CEV process provides a valid description of the dynamics of the Hong Kong dollar exchange rate. This information gives us a better understanding of the linked exchange rate system of Hong Kong dollar and other applications such as currency option pricing with target zone feature. The second part describes the method, through similarity transformations, of finding a first-passage-time (FPT) distribution associated with two boundaries of an underlying asset following CEV process. There are wide applications of the FPT distribution in the quantitative finance. For instance, many exotic options of path dependent nature are closely related to the FPT distribution. / Detailed summary in vernacular field only. / Chu, Shek Wai = 以不變方差彈性隨機過程建模港元聯繫匯率制度 / 朱石惠. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 92-95). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Chu, Shek Wai = Yi bu bian fang cha tan xing sui ji guo cheng jian mo Gang yuan lian xi hui lu zhi du / Zhu Shihui. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview --- p.1 / Chapter 1.2 --- Hong Kong Dollar Linked Exchange Rate System and Quasi-Bounded Processes --- p.3 / Chapter 1.3 --- CEV Processes and CEV Options Pricing Model --- p.4 / Chapter 2 --- Literature Reviews of Exchange Rate Modelling --- p.7 / Chapter 2.1 --- Krugman’s Model --- p.7 / Chapter 2.2 --- Jong, Drost, and Werker’s Model (Jump-diffusion Model) --- p.8 / Chapter 2.3 --- Larsen and Sorensen’s Model (Jacobi Diffusion Model) --- p.10 / Chapter 2.4 --- Ingersoll’s Model --- p.11 / Chapter 2.5 --- Summary --- p.12 / Chapter 3 --- Modelling HKD Exchange Rate by CEV Processes --- p.14 / Chapter 3.1 --- Introduction --- p.14 / Chapter 3.2 --- Principle Of Maximum Likelihood Estimation --- p.16 / Chapter 3.2.1 --- Definition of Likelihood --- p.17 / Chapter 3.2.2 --- Properties of Maximum Likelihood Estimators --- p.19 / Chapter 3.2.3 --- Estimating Asymptotic Variance of Maximum Likelihood Estimators --- p.22 / Chapter 3.2.4 --- Discrete-time Econometric Specification --- p.23 / Chapter 3.2.5 --- The Numerical Optimization Algorithm --- p.24 / Chapter 3.3 --- Quasi-bounded CEV Model --- p.25 / Chapter 3.3.1 --- Hong Kong Exchange Rate Data --- p.26 / Chapter 3.3.2 --- Quasi-bounded Property of CEV Model --- p.29 / Chapter 3.4 --- The Estimation Results and Conclusions --- p.37 / Chapter 3.4.1 --- Introduction --- p.37 / Chapter 3.4.2 --- Square Root Processes --- p.38 / Chapter 3.4.3 --- Constant Elasticity of Variance Processes --- p.45 / Chapter 3.4.4 --- Summary of results --- p.51 / Chapter 4 --- CEV Exotic Options Pricing --- p.54 / Chapter 4.1 --- Introduction --- p.54 / Chapter 4.1.1 --- Barrier Options --- p.55 / Chapter 4.1.2 --- Lookback Options --- p.56 / Chapter 4.2 --- CEV Probability Density Function --- p.58 / Chapter 4.2.1 --- Conditional Probability Density Function --- p.58 / Chapter 4.2.2 --- Interpolation Scheme, Estimates and Bounds --- p.66 / Chapter 4.2.3 --- Multi-Stage Approximation Scheme --- p.68 / Chapter 4.3 --- Pricing CEV Exotic Options --- p.70 / Chapter 4.3.1 --- Pricing barrier options and numerical examples --- p.70 / Chapter 4.3.2 --- Pricing lookback options and numerical examples --- p.74 / Chapter 4.4 --- Sensitivity Analysis --- p.78 / Chapter 4.4.1 --- Analysis for up-and-out call option --- p.80 / Chapter 4.4.2 --- Analysis for Floating strike lookback put option --- p.86 / Bibliography --- p.92