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

published_or_final_version / Economics / Master / Master of Social Sciences

M.Comm. / Chapter 2 discussed the basic principles underlying of the two major option pricing formulae. It clearly showed that two totally different approaches were followed in each case, and yet both arrived at approximately the same value for the price of an option. Both these approaches made certain assumptions in their derivation of the formulae in order to simplify the final expressions, and to produce a more workable solution. They both however made substantial use of statistical probability in order to determine the likelihood of a certain event occurring. Chapter 3 gave a detailed derivation of both the Black and Scholes and the Binomial tree pricing formulae, as well as the associated criticism and advantages of the respective approaches. Value at risk, or VaR, was used in determining the statistical probability of a certain portfolio consisting of a specified option losing more than a certain percentage of its value over a given period of time. The resulting number obtained can be used to judge the riskiness of a portfolio in the given market conditions. All of these formulae are used on a daily basis by financial professionals in the daily operations of a magnitude of different institutions in order to value financial portfolios, the risk associated with these portfolios and the probability of certain events occurring within the portfolios in order to make better decisions and increase the profitability of these institutions, without actually knowing the underlying principles. - As- such these --formulae merely become a number crunching business, and interpretation of these numbers, without realising the pitfalls associated with the approaches in establishing these formulae. The random walk theory for unrestricted movement assumes that at t=0, the rates are at the origin. This can be interpreted as 0%, and instinctively any person would agree that 0% is not possible in any fixed income environment, due to the time value attached to money. Choosing the ruling rate as the origin would be more practical in determining the origin, but care must be taken in assigning probabilities to the up and down movements. At the onset of the problems amongst the emerging markets during 1998, the probability of rates increasing once it reached 17,00% was much higher than that of the rates decreasing. However, barely a month later when the rates had reached its peak at more than 21,00% and were declining again, the probability of the rates increasing once it reached 17,00% again was much lower than that of it decreasing further. This would have a significant effect on the probability generating function, and hence also an effect on the mean and variance thus derived. The probability curve of the rates during these times were also not represented by a standard normal curve, and as such the heteroscedacity of the curve had a major influence on the pricing of options. During extreme periods both the random walk theory and the Wiener process would be totally skewed, and unreliable answers would be derived from this approach. By 'adjusting the expression for a non-standard distribution, these problems can be eliminated and an accurate approach once again obtained using this process. Problems that could occur when using this approach to solve inaccuracies would amongst others include the following: The incorrect distribution function is being applied for the specific set of conditions prevailing in the market. This is due to the fact that under these abnormal conditions the distribution function can change over a very short period of time. Incorrect skews being applied to the distribution function due to fast changing market conditions. When to revert back to the normal distribution function. It then becomes a question not of an improper analytical approach, but incorrect timing approach. Since markets mostly perform according to the standardised normal distribution function the Wiener approach hold true for most applications.

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

Chan Chun Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 63-66). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Volatility Smile and Stochastic Volatility Models --- p.6 / Chapter 2.1 --- Volatility Smile --- p.6 / Chapter 2.2 --- Stochastic Volatility Model --- p.9 / Chapter 2.3 --- Multiscale Stochastic Volatility Model --- p.12 / Chapter 3 --- Lookback Options --- p.14 / Chapter 3.1 --- Lookback Options --- p.14 / Chapter 3.2 --- Lookback Spread Option --- p.15 / Chapter 3.3 --- Dynamic Fund Protection --- p.16 / Chapter 3.4 --- Floating Strike Lookback Options under Black-Scholes Model --- p.17 / Chapter 4 --- Floating Strike Lookback Options under Multiscale Stochastic Volatility Model --- p.21 / Chapter 4.1 --- Multiscale Stochastic Volatility Model --- p.22 / Chapter 4.1.1 --- Model Settings --- p.22 / Chapter 4.1.2 --- Partial Differential Equation for Lookbacks --- p.24 / Chapter 4.2 --- Pricing Lookbacks in Multiscale Asymtoeics --- p.26 / Chapter 4.2.1 --- Fast Tirnescale Asymtotics --- p.28 / Chapter 4.2.2 --- Slow Tirnescale Asymtotics --- p.31 / Chapter 4.2.3 --- Price Approximation --- p.33 / Chapter 4.2.4 --- Estimation of Approximation Errors --- p.36 / Chapter 4.3 --- Floating Strike Lookback Options --- p.37 / Chapter 4.3.1 --- Accuracy for the Price Approximation --- p.39 / Chapter 4.4 --- Calibration --- p.40 / Chapter 5 --- Other Lookback Products --- p.43 / Chapter 5.1 --- Fixed Strike Lookback Options --- p.43 / Chapter 5.2 --- Lookback Spread Option --- p.44 / Chapter 5.3 --- Dynamic Fund Protection --- p.45 / Chapter 6 --- Numerical Results --- p.49 / Chapter 7 --- Conclusion --- p.53 / Appendix --- p.55 / Chapter A --- Verifications --- p.55 / Chapter A.1 --- Formula (4.12) --- p.55 / Chapter A.2 --- Formula (4.22) --- p.56 / Chapter B --- Proof of Proposition --- p.57 / Chapter B.1 --- Proof of Proposition (4.2.2) --- p.57 / Chapter C --- Black-Scholes Greeks for Lookback Options --- p.60 / Bibliography --- p.63

Gao, Fei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 52-53). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Option Pricing with GARCH --- p.1 / Chapter 1.2 --- Mean Reversion in GARCH --- p.3 / Chapter 1.3 --- Thesis Setting --- p.4 / Chapter 2 --- Literature Review --- p.5 / Chapter 2.1 --- GARCH Model --- p.5 / Chapter 2.2 --- Locally Risk-Neutral Valuation --- p.8 / Chapter 2.3 --- Conditional Esscher Transform --- p.9 / Chapter 3 --- The Model --- p.12 / Chapter 3.1 --- The Mean-Reverting GARCH Model --- p.12 / Chapter 3.2 --- The Characteristic Functions --- p.15 / Chapter 3.3 --- Identification of Pricing Measures --- p.21 / Chapter 3.3.1 --- Conditional Esscher Transform --- p.21 / Chapter 3.3.2 --- Our Proposed Change of Measure --- p.25 / Chapter 4 --- Option Pricing --- p.30 / Chapter 4.1 --- Fast Fourier Transform --- p.30 / Chapter 4.2 --- Option on Futures : --- p.32 / Chapter 4.3 --- Numerical Analysis --- p.35 / Chapter 5 --- Empirical Analysis - Application to the crude oil market --- p.37 / Chapter 5.1 --- Description of data --- p.37 / Chapter 5.2 --- Estimation --- p.38 / Chapter 5.3 --- Comparisons --- p.40 / Chapter 6 --- Summary and Future work --- p.42 / Chapter 7 --- Appendix --- p.43 / Bibliography --- p.52