published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

In the first essay, this thesis provides a new methodology for pricing the fixed income derivatives using the arbitrage-free Heath-Jarrow-Morton model (hereafter HJM model). While, most previous empirical implementations of HJM model like that by Amin and Morton (1994) are focused on one-factor model only, the essay attempts to extend the test to a two-factor model that could further capture the subtleties of the forward rate process. The two-factor Poisson-Gaussian version of HJM model derived by Das (1999) that incorporates a jump component as the second state variables is used to value the actively traded Eurodollar futures call option under the jump diffusion lattice. The one-factor and two-factor models are compared with five volatility functions to evaluate the degree of pricing improvement by the inclusion of one more state variable. / The essay also addresses the critical issues on the volatility structure of forward rates that affect the pricing performance of option under the HJM framework. Three new volatility specifications are constructed to estimate the traded options. The first volatility function is the humped & curvature adjusted model that allows for humped shape in volatility structure and better adjustment to the curvature of the term structure. The second is the humped & proportional model that exhibits humped volatility feature and is proportional to the forward rate. The third function is the linear exponential model that is extended from Vasicek's exponential model. They are compared with two other volatility structures developed by previous researchers on their pricing performances. The alternative models are examined from the perspectives of in-sample fit, out-of-sample pricing and hedging. / The second essay develops an approach for estimating the Value-at-Risk (hereafter VaR) with jumps using the Monte Carlo simulation method. It is by far the first paper to estimate VaR using the HJM model. The paper takes the framework of the Poisson Gaussian version of HJM model (hereafter, HJM jump-diffusion model) from Das (1999). The model is incorporated with a jump component to capture the kurtosis effect in the daily price changes. As a result, the HJM jump-diffusion model allows for the fat tailed and skewed distribution of return in most financial markets. The simulation process is expedited by using variance reduction method. The model is used for calculating the VaR of a portfolio consisting of the fixed income derivatives. The accuracy of the VaR estimates is examined statistically at the VaR at confidence level of both 95 and 99 percent. / This thesis is a collection of two essays that explore issues related to the pricing and the risk management of fixed income securities and derivatives in US markets. In the context of the pricing of derivatives, the arbitrage-free pricing approach is adopted. For the issue of risk management, the estimation of Value-at-Risk is presented. / by Ze-To Yau Man. / Source: Dissertation Abstracts International, Volume: 62-09, Section: A, page: 3138. / Supervisors: Jia He; Ying-foon Chow. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (p. 145-151). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

by Chan Chi-man, Simon. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves [5]-[8] (2nd group)). / ACKNOWLEDGMENTS --- p.i / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.iv / LIST OF FIGURES --- p.vii / LIST OF TABLES --- p.viii / Chapter CHAPTER I. --- INTRODUCTION --- p.1 / Background --- p.1 / Objectives --- p.3 / Scope --- p.5 / Organization of the Paper --- p.6 / Chapter CHAPTER II. --- THE HONG KONG STOCK MARKET - QUANTIFYING ITS CHARACTERISTICS --- p.7 / Introduction --- p.7 / Choice of Proxy for the Market --- p.9 / Hong Kong in the Asian Pacific Region --- p.11 / Choice of Benchmarks for Comparisons --- p.12 / Comparative Returns and Standard Deviations --- p.13 / Correlations Amongst Different Markets --- p.16 / Comparative Price to Earnings (P/E) Ratios --- p.18 / Market Liquidity --- p.19 / Market Concentration --- p.20 / Summary --- p.21 / Chapter CHAPTER III. --- PRICING OF RISKY ASSETS IN HONG KONG --- p.23 / Introduction --- p.23 / Applicability of Pricing Models in the Hong Kong Stock Market --- p.23 / Literature Review --- p.23 / CAPM --- p.28 / The model --- p.28 / Hypotheses to be tested --- p.29 / Data --- p.30 / Methodology --- p.30 / Portfolio construction --- p.30 / Variable estimation --- p.31 / Cross-sectional regressions --- p.31 / Results and discussions --- p.32 / Stability of Beta --- p.34 / APT --- p.37 / Introduction --- p.37 / Analysis --- p.38 / Chapter CHAPTER IV. --- THE EFFICIENCY AND ANOMALIES OF THE HONG KONG STOCK / MARKET --- p.51 / Market Efficiency --- p.51 / Introduction --- p.51 / Informational Efficiency --- p.51 / Forms of market efficiency --- p.52 / Empirical evidence in Hong Kong --- p.53 / Historical prices --- p.53 / Investment advisory --- p.54 / Government budget speeches --- p.55 / Takeover --- p.55 / Conclusions --- p.55 / Anomalies --- p.56 / Introduction --- p.56 / An Exercise on PBV --- p.57 / Summary --- p.58 / Chapter CHAPTER V. --- POLITICAL INFLUENCE AND THE STOCK MARKET --- p.59 / Introduction --- p.59 / Literature Review --- p.60 / Political Risk in Hong Kong --- p.61 / Conclusion --- p.64 / Chapter CHAPTER VI. --- DIVERSIFICATION --- p.65 / Introduction --- p.65 / Literature Review --- p.65 / Does International Diversification Work --- p.67 / Conclusion --- p.72 / Chapter CHAPTER VII. --- CONCLUSIONS --- p.73 / What Moves Stock Prices? --- p.74 / Is the Stock Market Overreacting? --- p.75 / Some Suggestions --- p.76 / APPENDICES / BIBLIOGRAPHY

Guan, Peiqiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 67-71). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.6 / Chapter 2.1 --- Characteristic Function --- p.6 / Chapter 2.1.1 --- Definition --- p.6 / Chapter 2.1.2 --- Inverse Fourier Transform --- p.8 / Chapter 2.1.3 --- Fast Fourier Transform (FFT) --- p.9 / Chapter 2.2 --- Levy Processes --- p.13 / Chapter 2.2.1 --- Definition --- p.13 / Chapter 2.2.2 --- Levy-Khinchine Formula --- p.15 / Chapter 2.2.3 --- Levy Processes in Finance --- p.17 / Chapter 2.3 --- Exotic Options --- p.17 / Chapter 2.3.1 --- Barrier Options --- p.18 / Chapter 2.3.2 --- Lookback Options --- p.19 / Chapter 2.3.3 --- Asian Options --- p.20 / Chapter 3 --- FFT Network Model --- p.23 / Chapter 3.1 --- Weaknesses of Traditional Tree Approaches --- p.24 / Chapter 3.2 --- FFT Network Model --- p.30 / Chapter 3.3 --- Basic Transition Probability Matrix --- p.31 / Chapter 3.4 --- Basic FFT Network Pricing Algorithm --- p.35 / Chapter 3.4.1 --- Plain Vanilla Options --- p.35 / Chapter 4 --- FFT Network for Exotic Options --- p.38 / Chapter 4.1 --- Barrier Option Pricing --- p.38 / Chapter 4.2 --- Forward Shooting Grid --- p.41 / Chapter 4.3 --- FSG in FFT Network --- p.43 / Chapter 4.4 --- Lookback and Knock-in Options --- p.45 / Chapter 4.4.1 --- American Lookback Option Pricing Algorithm --- p.48 / Chapter 4.4.2 --- Knock-in American Option Pricing Algorithm --- p.50 / Chapter 4.5 --- Asian Option Pricing --- p.51 / Chapter 4.5.1 --- Asian Option Pricing Algorithm --- p.54 / Chapter 5 --- Numerical Implementation --- p.57 / Chapter 5.1 --- Numerical Scheme --- p.57 / Chapter 5.2 --- Numerical Result --- p.60 / Chapter 6 --- Conclusion --- p.65 / Bibliography --- p.67

Chan, Tsz Him. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 94-96). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Monte Carlo method in Finance --- p.6 / Chapter 2.1 --- Principle of MC and pricing theory --- p.6 / Chapter 2.2 --- An illustrative example --- p.9 / Chapter 3 --- Discretization method --- p.15 / Chapter 3.1 --- The Euler scheme and Milstein scheme --- p.16 / Chapter 3.2 --- Convergence of Mean Square Error --- p.19 / Chapter 4 --- Quasi Monte Carlo method --- p.22 / Chapter 4.1 --- Basic idea of QMC --- p.23 / Chapter 4.2 --- Application of QMC in Finance --- p.29 / Chapter 4.3 --- Another illustrative example --- p.34 / Chapter 5 --- Our Methodology --- p.42 / Chapter 5.1 --- Measure decomposition --- p.43 / Chapter 5.2 --- QMC in SDE simulation --- p.51 / Chapter 5.3 --- Towards a workable algorithm --- p.58 / Chapter 6 --- Numerical Result --- p.69 / Chapter 6.1 --- Case I Generalized Wiener Process --- p.69 / Chapter 6.2 --- Case II Geometric Brownian Motion --- p.76 / Chapter 6.3 --- Case III Ornstein-Uhlenbeck Process --- p.83 / Chapter 7 --- Conclusion --- p.91 / Bibliography --- p.96

Cheng, Ping. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 91-96). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.1.1 --- Accumulator in a Nutshell --- p.1 / Chapter 1.1.2 --- Criticism over Accumulators --- p.3 / Chapter 1.1.3 --- Significance of Research over Accumulators --- p.4 / Chapter 1.1.4 --- Contribution of this Research --- p.5 / Chapter 1.2 --- Literature Review --- p.6 / Chapter 1.2.1 --- Literature on Option Pricing Theory --- p.6 / Chapter 1.2.2 --- Literature on Occupation Time Derivatives and Accumulators --- p.9 / Chapter 1.2.3 --- Accumulators as Occupation Time Deriva- tives --- p.14 / Chapter 1.3 --- Structure of this Thesis --- p.16 / Chapter 2 --- Theoretical Foundation --- p.17 / Chapter 2.1 --- Black Scholes Framework --- p.18 / Chapter 2.1.1 --- The Model --- p.18 / Chapter 2.1.2 --- Girsanov's Theorem --- p.20 / Chapter 2.1.3 --- Simulation --- p.21 / Chapter 2.2 --- Heston Framework --- p.22 / Chapter 2.2.1 --- Motivation to Extend to Heston Model --- p.22 / Chapter 2.2.2 --- The Model --- p.23 / Chapter 2.2.3 --- The Monte Carlo Method --- p.25 / Chapter 3 --- Pricing under Black-Scholes Framework --- p.30 / Chapter 3.1 --- Structure One (Suspension Feature) --- p.30 / Chapter 3.1.1 --- Introduction --- p.30 / Chapter 3.1.2 --- Model --- p.32 / Chapter 3.1.3 --- Sensitivity Tests --- p.35 / Chapter 3.1.4 --- Simulation Results --- p.38 / Chapter 3.2 --- Structure Two (Knock-out Feature) --- p.40 / Chapter 3.2.1 --- Introduction --- p.40 / Chapter 3.2.2 --- Model --- p.41 / Chapter 3.2.3 --- Sensitivity Tests --- p.45 / Chapter 3.2.4 --- Simulation Results --- p.48 / Chapter 3.3 --- Structure Three (Knock-out & Double Commit- ment Feature) --- p.50 / Chapter 3.3.1 --- Introduction --- p.50 / Chapter 3.3.2 --- Model --- p.51 / Chapter 3.3.3 --- Sensitivity Tests --- p.56 / Chapter 3.3.4 --- Simulation Results --- p.58 / Chapter 4 --- Extension: Pricing under Heston Framework --- p.59 / Chapter 4.1 --- Structure One --- p.59 / Chapter 4.1.1 --- Pricing of the Contract --- p.59 / Chapter 4.2 --- Structure Two and Three --- p.61 / Chapter 4.2.1 --- Simulation Results --- p.62 / Chapter 4.3 --- Heston Parameters Estimates --- p.63 / Chapter 5 --- Discussion --- p.66 / Chapter 5.1 --- Volatility of Accumulators --- p.66 / Chapter 5.2 --- Instability in the Model Parameters --- p.69 / Chapter 5.3 --- Premium over Accumulators --- p.71 / Chapter 5.4 --- Return of the Accumulator Products --- p.72 / Chapter 6 --- Future Work & Conclusion --- p.75 / Chapter 6.1 --- Future Work --- p.75 / Chapter 6.2 --- Conclusion --- p.76 / Chapter A --- Other Parameters Estimation --- p.77 / Chapter B --- Sample Contracts --- p.80 / Chapter B.1 --- Equity Accumulator --- p.80 / Chapter B.2 --- Commodity Accumulator --- p.80 / Chapter B.3 --- FX-Linked Accumulation --- p.80 / Bibliography --- p.91

This dissertation examines whether Percs, Preferred Equity Redemption Cumulative Stocks, are properly priced regarding to the relevant securities, such as the underlying common stock, the long-term call option of the stock, and so on. Test results indicate that Percs were overpriced with respect to the equivalent packages composed of the relevant securities. Further tests on arbitrage restrictions show that transaction costs would prevent arbitrage profits. This dissertation also examines the market reactions to Percs offerings. Test results reveal that the market reactions to the announcement of Percs offering and the actual issuance are both significantly negative. Compared to the market reaction on common stock offering announcement, the market reaction on Percs offering announcement is weaker. The overpricing of Percs and the weaker reaction of the market suggest that Percs may have advantages in transaction costs, taxes and some corporate finance issues.

This thesis comprises three essays that explore several theoretical and empirical features of affine term structure models. In the first essay, we focus on the ability of continuous-time affine term structure models to capture time variability in the second conditional moment. Using data on US Treasury yields, we conclude that affine term structure models are much better at extracting time-series volatility from the cross-section of yields than argued in the literature. These models have nonetheless difficulty capturing volatility dynamics at the short end of the maturity spectrum, perhaps indicating some form of segmentation between long-maturity and short-maturity bonds. These results are robust to the choice of sample period, interpolation method and estimation method. In the second essay, we propose the use of the unscented Kalman filter technique for the estimation of affine term structure models using non-linear instruments. We focus on swap rates and show that the unscented Kalman filter leads to important reductions in bias and gains in precision. The use of the unscented Kalman filter results in substantial improvements in out-of-sample forecasts. Our findings suggest that the unscented Kalman filter may prove to be a good approach for a number of problems in fixed income pricing in which the relationship between the state vector and the observations is nonlinear, such as the estimation of term structure models using interest rate derivatives or coupon bonds, and the estimation of quadratic term structure models. The third essay provides a tractable framework for pricing defaultable securities with recovery risk. Pricing solutions are explored for a large family of discrete-time affine processes and a five-factor Gaussian model is estimated on BBB and B Standard and Poor's yield indices. This rich econometric setup allows the model to simultaneously capture two important stylized facts of defaultable securities: The positive correlation between the loss given default and the intensity of default, and the negative correlation between the intensity of default and the risk-free interest rate.

American options are the most commonly traded financial derivatives in the market. Pricing these options fairly, so as to avoid arbitrage, is of paramount importance. Closed form solutions for American put options cannot be utilised in practice and so numerical techniques are employed. This thesis looks at the work done by other researchers to find an analytic solution to the American put option pricing problem and suggests a practical method, that uses Monte Carlo simulation, to approximate the American put option price. The theory behind option pricing is first discussed using a discrete model. Once the concepts of arbitrage-free pricing and hedging have been dealt with, this model is extended to a continuous-time setting. Martingale theory is introduced to put the option pricing theory in a more formal framework. The construction of a hedging portfolio is discussed in detail and it is shown how financial derivatives are priced according to a unique riskneutral probability measure. Black-Scholes model is discussed and utilised to find closed form solutions to European style options. American options are discussed in detail and it is shown that under certain conditions, American style options can be solved according to closed form solutions. Various numerical techniques are presented to approximate the true American put option price. Chief among these methods is the Richardson extrapolation on a sequence of Bermudan options method that was developed by Geske and Johnson. This model is extended to a Repeated-Richardson extrapolation technique. Finally, a Monte Carlo simulation is used to approximate Bermudan put options. These values are then extrapolated to approximate the price of an American put option. The use of extrapolation techniques was hampered by the presence of non-uniform convergence of the Bermudan put option sequence. When convergence was uniform, the approximations were accurate up to a few cents difference.

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