published_or_final_version / abstract / Statistics and Actuarial Science / Master / Master of Philosophy

Liu Zheng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 69-72). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Contributions --- p.2 / Chapter 1.2 --- Dissertation Organization --- p.3 / Chapter 2 --- Problem Statement and Background Study --- p.4 / Chapter 2.1 --- Problem Statement --- p.4 / Chapter 2.2 --- Background Study --- p.6 / Chapter 2.2.1 --- Overview of Pattern Discovery Methods --- p.7 / Chapter 2.2.2 --- Applications --- p.9 / Chapter 3 --- Ball Discovery Algorithms --- p.13 / Chapter 3.1 --- Brute-force Method for Ball Discovery --- p.13 / Chapter 3.2 --- Ball Discovery with Small Point Sets --- p.15 / Chapter 3.2.1 --- Pruning the Search Space Using RP-tree --- p.15 / Chapter 3.2.2 --- CB-tree - Collection of Balls in a Compact and Complete Form --- p.22 / Chapter 3.2.3 --- Algorithm of Finding Balls Using RP-tree and CB-tree --- p.31 / Chapter 3.3 --- Ball Discovery in Large Point Sets --- p.31 / Chapter 3.3.1 --- Candidate Sets of Balls --- p.31 / Chapter 3.3.2 --- A Divide-and-Conquer Algorithm --- p.35 / Chapter 3.4 --- Heuristic Greedy Algorithms for Ball Discovery --- p.37 / Chapter 3.4.1 --- A Heuristic Greedy Algorithm --- p.37 / Chapter 3.4.2 --- Another Heuristic Greedy Algorithm --- p.38 / Chapter 4 --- Evaluations --- p.40 / Chapter 5 --- Discussion --- p.59 / Chapter 5.1 --- Order and Index the Points --- p.59 / Chapter 5.2 --- Incremental Points Update --- p.59 / Chapter 5.3 --- Smallest Enclosed Ball Algorithm --- p.60 / Chapter 6 --- Conclusion and Future Research --- p.61 / Chapter A --- Appendix --- p.63 / Chapter A.1 --- Fundamental Algorithms --- p.63 / Chapter A.1.1 --- Computing Smallest Enclosed Ball of a Point Set in Euclidean Space --- p.63 / Chapter A.1.2 --- Finding All Cliques of an Undirected Graph --- p.65 / Chapter A.2 --- An Example of a Small Data Set --- p.66 / Bibliography --- p.69

Leong U Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 32-34). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Structural Bond Pricing Models --- p.5 / Chapter 2.1 --- The Merton Model --- p.5 / Chapter 2.2 --- Extended Merton Model --- p.6 / Chapter 2.3 --- Longstaff and Schwartz Model --- p.8 / Chapter 3 --- Methodology --- p.11 / Chapter 3.1 --- Maximum Likelihood Estimation --- p.13 / Chapter 3.2 --- Non-linear Filtering Process --- p.13 / Chapter 3.3 --- Modification for LS Model --- p.15 / Chapter 4 --- Simulation and Empirical Analysis --- p.16 / Chapter 4.1 --- Simulation Study --- p.16 / Chapter 4.2 --- Empirical Analysis --- p.19 / Chapter 4.2.1 --- Bond Selection --- p.19 / Chapter 4.2.2 --- Result for EM Model --- p.21 / Chapter 4.2.3 --- Result for LS Model --- p.24 / Chapter 4.3 --- Implications from Empirical Analysis --- p.28 / Chapter 5 --- Conclusion --- p.30 / Bibliography --- p.32

published_or_final_version / Business / Master / Master of Philosophy

Numerous studies of the behavior of speculative prices have shown that the empirical distribution of such returns is consistently more peaked and fat-tailed than a Gaussian, and often positively skewed. Strong evidence is presented indicating hat such returns are better modeled by two-and three-component normal mixtures. By varying the means, variances, and probability weights of the component normals, a wide variety of peaked, fat-tailed, and symmetric or skewed distributions may be represented with very tractable mathematical expressions. Examination of the returns of 116 CBOE firms over three two-year periods indicates a high percentage of good fits for such normal mixtures, based on the chi-square statistic. Further, inspection of the parameters estimated for the two-component normal mixture reveals that the larger variance is quite frequently not associated with the lower probability weight as hypothesized by Mandelbrot and others. A new method of selecting class-boundaries is proposed to improve the reliability of the chi-square goodness-of-fit test. Using simulation, this method is found to be superior to the traditional Mann-Wald equiprobable approach, particularly for low priced securities. Using the assumption of risk-neutrality and a mixture of normals density for the underlying security returns, the mixture call option pricing model is derived. Call option prices are shown to be weighted sums of Black-Scholes prices, with solutions to the mixture model converging to Black-Scholes prices, with solutions to the mixture model converging to Black-Scholes solutions as the number of periods to expiration becomes large. Using the parameters obtained from typical mixture densities of actual CBOE firms, mixture model prices are generated and compared with Black-Scholes prices. It is found that out of the money, near term options are underpriced by Black-Scholes relative to the mixture model. The closer to expiration and the farther out of the money the option, the more Black-Scholes under-prices relative to the mixture model. Additionally, the fatter tailed and more positively skewed the underlying security returns distribution, the greater the differences between the two call option pricing models.

No description available.

No description available.

No description available.

No description available.

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