published_or_final_version / abstract / Real Estate and Construction / Doctoral / Doctor of Philosophy

published_or_final_version / Economics and Finance / Doctoral / Doctor of Philosophy

by Ka-kit Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 71-73). / Chapter I. --- Introduction to Stochastic Calculus --- p.1 / Stochastic Processes --- p.2 / Stochastic Integration --- p.6 / Quadratic Variation Processes and Mutual Variation Process --- p.11 / The Ito Formula --- p.13 / Girsanov's Theorem --- p.16 / Stochastic Differential Equations --- p.18 / Chapter II. --- Pricing American Equity Options --- p.21 / A Representation Formula for European Put Option --- p.22 / The Free Boundary Formulation of American Put Option --- p.24 / A Representation Formula for American Put Option --- p.27 / An Alternative Representation Formula for American Put Option --- p.35 / The Optimal Exercise Boundary --- p.37 / Numerical Valuations of the Representation Formulae --- p.39 / Chapter III. --- The Effects of Margin Requirements on Option Prices --- p.42 / Pricing European Options --- p.44 / Pricing American Options --- p.46 / Chapter IV. --- General Pricing Theory --- p.49 / Transformations of Price Processes --- p.50 / No Arbitrage Condition and Completeness of Market --- p.52 / More on Market Completeness --- p.58 / Term Structure of Interest Rate and Interest Rate Options --- p.61 / Pricing Equity Options --- p.67 / Bibliography --- p.71

by Fu Yiu-Hang. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 66-67). / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.ii / LIST OF TABLES --- p.vi / LIST OF EXHIBITS --- p.vii / PREFACE --- p.viii / ACKNOWLEDGMENTS --- p.x / Chapter / Chapter I. --- INTRODUCTION --- p.1 / What is an Option? --- p.1 / Options Market --- p.2 / Uses of Options --- p.2 / Value of Options --- p.3 / Index Options --- p.4 / Hang Seng Index Options --- p.4 / Chapter II. --- BASIC PROPERTIES OF OPTIONS --- p.5 / Assumptions --- p.5 / Notation --- p.5 / Option Prices at Expiration --- p.6 / Call Option Prices at Expiration --- p.6 / Put Option Prices at Expiration --- p.6 / Upper Bounds for Option Prices --- p.6 / Upper Bounds for Call Option Prices --- p.6 / Upper Bounds for Put Option Prices --- p.6 / Lower Bounds for European Option Prices --- p.7 / Lower Bounds for European Call Option Prices --- p.7 / Lower Bounds for European Put Option Prices --- p.8 / Put-Call Parity --- p.8 / Chapter III. --- FACTORS AFFECTING OPTION PRICES --- p.10 / Price of Underlying Instrument --- p.10 / Exercise Price of the Option --- p.10 / Volatility of the Price of Underlying Instrument --- p.11 / Time to Expiration --- p.11 / Risk-free Rate --- p.11 / Dividends --- p.12 / Chapter IV. --- OPTION PRICING MODEL --- p.13 / Assumptions --- p.13 / The Price of Underlying Instrument Follows a Lognormal Distribution --- p.13 / The Variance of the Rate of Return of Underlying Instrument is a Constant --- p.17 / The Risk-free Rate is a Constant --- p.19 / No Dividends are Paid --- p.20 / There are No Transaction Costs and Taxes --- p.20 / The Black-Scholes Option Pricing Model --- p.21 / Notation --- p.21 / The Formulas --- p.21 / The Variables --- p.22 / Properties of the Black-Scholes Formulas --- p.22 / Implied Volatility --- p.23 / Bias of the Black-Scholes Option Pricing Model --- p.26 / Other Option Pricing Models。……………… --- p.27 / Chapter V. --- SENSITIVITIES OF OPTION PRICE TO ITS FACTORS --- p.29 / Delta --- p.29 / Vega --- p.30 / Theta --- p.31 / Rho --- p.32 / Gamma --- p.33 / Managing the Change in the Value of Option --- p.34 / Sensitivities of Portfolio Value to the Factors --- p.34 / Chapter VI. --- TRADING STRATEGIES OF OPTIONS --- p.35 / Methodology --- p.35 / Limitations --- p.36 / Basic Strategies --- p.37 / Long Call --- p.37 / Short Call --- p.39 / Long Put --- p.40 / Short Put --- p.42 / Spread Strategies --- p.43 / Money Spread --- p.43 / Ratio Spread --- p.46 / Box Spread --- p.46 / Butterfly Spread --- p.46 / Condor --- p.49 / Calendar Spread --- p.49 / Diagonal Spread --- p.52 / Combination Strategies --- p.52 / Straddle --- p.52 / Strap --- p.54 / Strip --- p.54 / Strangle --- p.54 / Selecting Trading Strategies Intelligently --- p.56 / Chapter VII. --- CONCLUSIONS --- p.57 / APPENDICES --- p.60 / BIBLIOGRAPHY --- p.66

Lau, Ka Yung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 78-79). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background --- p.5 / Chapter 2.1 --- Jump Diffusion Models --- p.6 / Chapter 2.2 --- Double Exponential Jump Diffusion Model --- p.8 / Chapter 3 --- Option Pricing with DEJD --- p.10 / Chapter 3.1 --- Laplace Transform --- p.10 / Chapter 3.2 --- European Option Pricing --- p.13 / Chapter 3.3 --- Barrier Option Pricing --- p.14 / Chapter 3.4 --- Lookback Options --- p.16 / Chapter 3.5 --- Turbo Warrant --- p.17 / Chapter 3.6 --- Numerical Examples --- p.26 / Chapter 4 --- Quanto Options under DEJD --- p.30 / Chapter 4.1 --- Domestic Risk-neutral Dynamics --- p.31 / Chapter 4.2 --- The Exponential Copula --- p.33 / Chapter 4.3 --- The moment generating function --- p.36 / Chapter 4.4 --- European Quanto Options --- p.38 / Chapter 4.4.1 --- Floating Exchange Rate Foreign Equity Call --- p.38 / Chapter 4.4.2 --- Fixed Exchange Rate Foreign Equity Call --- p.40 / Chapter 4.4.3 --- Domestic Foreign Equity Call --- p.42 / Chapter 4.4.4 --- Joint Quanto Call --- p.43 / Chapter 4.5 --- Numerical Examples --- p.45 / Chapter 5 --- Path-Dependent Quanto Options --- p.48 / Chapter 5.1 --- The Domestic Equivalent Asset --- p.48 / Chapter 5.1.1 --- Mathematical Results on the First Passage Time of the Mixture Exponential Jump Diffusion Model --- p.50 / Chapter 5.2 --- Quanto Lookback Option --- p.54 / Chapter 5.3 --- Quanto Barrier Option --- p.57 / Chapter 5.4 --- Numerical results --- p.61 / Chapter 6 --- Conclusion --- p.64 / Chapter A --- Numerical Laplace Inversion for Turbo Warrants --- p.66 / Chapter B --- The Relation Among Barrier Options --- p.69 / Chapter C --- Proof of Lemma 51 --- p.71 / Chapter D --- Proof of Theorem 5.4 and 5.5 --- p.74 / Bibliography --- p.78

Ma Kai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 58-60). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Executive Options Repricing --- p.5 / Chapter 2.1 --- Plan Restrictions --- p.5 / Chapter 2.2 --- Corporate Governance Issues --- p.7 / Chapter 2.3 --- Securities Law Issues --- p.9 / Chapter 2.4 --- Accounting Issues --- p.10 / Chapter Chapter 3 --- Literature Review --- p.15 / Chapter 3.1 --- Options Repricing --- p.15 / Chapter 3.2 --- The Valuation of Executive Stock Options --- p.18 / Chapter 3.3 --- Extant Executive Stock Options Valuation Models --- p.19 / Chapter Chapter 4 --- Methodology --- p.23 / Chapter Chapter 5 --- Numerical Results --- p.26 / Chapter 5.1 --- Parameters Specification ´ؤ Base Case --- p.26 / Chapter 5.2 --- Value Line --- p.27 / Chapter 5.3 --- Incentive Effect --- p.28 / Chapter 5.4 --- Black-Scholes Neutral Repricing --- p.30 / Chapter Chapter 6 --- Parameters Sensitivity --- p.35 / Chapter 6.1 --- Compensation Package Composition --- p.35 / Chapter 6.2 --- Outside Wealth --- p.38 / Chapter 6.3 --- Beta --- p.41 / Chapter 6.4 --- Total Volatility of the Company Stock Price --- p.44 / Chapter 6.5 --- The Coefficient of the Constant Relative Risk Aversion of the Executive --- p.48 / Chapter Chapter 7 --- Conclusion --- p.51 / Appendix: Matlab Programs --- p.54 / References --- p.58 / Figures and Tables --- p.61

University of Macau / Faculty of Science and Technology / Department of Mathematics

This dissertation is a contribution to the pricing and portfolio choice theory in incomplete markets. It consists of three self-contained but interlinked essays. In the first essay, we present a utility-based methodology for the valuation and the risk management of mortgage-backed securities subject to totally unpredictable prepayment risk. Incompleteness stems from its embedded pre-payment option which affects the security's cash flow pattern. The prepayment time is constructed via deterministic or stochastic hazard rate. The relevant indifference price consists of a linear term, corresponding to the remaining outstanding balance, and a nonlinear one that incorporates the investor's risk aversion and the interest payments generated by the mortgage contract. The indifference valuation approach is also extended to the case of homogeneous mortgage pools. In the second essay, using forward optimality criteria, we analyze a portfolio choice problem when the local risk tolerance is time-dependent and asymptotically linear in wealth. This class corresponds to a dynamic extension of the traditional (static) risk tolerances associated with the power, logarithmic and exponential utilities. We provide explicit solutions for the optimal investment strategies and wealth processes in an incomplete non-Markovian market with asset prices modelled as Ito processes. The methodology allows for measuring the investment performance in terms of a benchmark and alter-native market views. In the last essay, we extend the forward investment performance approach to study the optimal portfolio choice problem in an incomplete market driven by jump processes. The asset price is modelled by a one-dimensional Lévy-Itô process. We prove the existence of a forward performance process by restricting the local risk tolerance functions to be time-independent and linear in wealth. This yields only three types of performance measurement criteria, namely, exponential, power and logarithmic. The optimal portfolios are constructed via stochastic feedback controls under these criteria. / text

published_or_final_version / Economics / Master / Master of Social Sciences

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