This thesis studies two subareas within the forecasting literature: volatility forecasting and risk-neutral density estimation and asks the question of how accurate volatility forecasts and risk-neutral density estimates can be made based on the given information. Two sources of information are employed to make those forecasts: historical information contained in time series of asset prices, and forward-looking information embedded in prices of traded options. Chapter 2 tests the comparative performance of two volatility scaling laws - the square-root-of-time (√T) and an empirical law, TH, characterized by the Hurst exponent (H) - where volatility is measured by sample standard deviation of returns, for forecasting the volatility term structure of crude oil price changes and ten foreign currency changes. We find that the empirical law is overall superior for crude oil, whereas the selection of a superior model is currency-specific and relative performance substantially differs across currencies. Our results are particularly important for regulatory risk management using Value-at-Risk and suggest the use of empirical law for volatility and quantile scaling. Chapter 3 studies the predictive ability of corridor implied volatility (CIV) measure. By adding CIV measures to the modified GARCH specifications, we show that narrow and mid-range CIVs outperform the wide CIVs, market volatility index and the BlackScholes implied volatility for horizons up to 21 days under various market conditions. Results of simulated trading reinforce our statistical findings. Chapter 4 compares six estimation methods for extracting risk-neutral densities (RND) from option prices. By using a pseudo-price based simulation, we find that the positive convolution approximation method provides the best performance, while mixture of two lognormals is the worst; In addition, we show that both price and volatility jumps are important components for option pricing. Our results have practical applications for policymakers as RNDs are important indicators to gauge market sentiment and expectations.

Huang Zhongbing. / "4 November, 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 123-131). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

by Ho Kwong-shing Lawrence. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 43-44). / ABSTRACT --- p.ii / TABLE OF CONTENTS --- p.iii / ACKNOWLEDGEMENT --- p.iv / CHAPTER / Chapter I. --- INTRODUCTION AND LITERATURE REVIEW --- p.1 / Chapter II. --- COMBINING SALES FORECASTS --- p.7 / Chapter III. --- EXPERIMENTAL DESIGN --- p.14 / Chapter IV. --- SIMULATION RESULTS --- p.19 / Chapter V. --- SUMMARY AND CONCLUSION --- p.27 / APPENDIX --- p.31 / BIBLIOGRAPHY --- p.43

by Chan Kwok Ming. / Chinese title in romanization: Yi wei xi tong re li xue xing zhi zhi Mengdikaluo yan jiu. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaf 69.

by Terry Shing-fong Lew. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 40-42). / Chapter Chapter 1 --- Introduction --- p.Page1 / Chapter Chapter 2 --- Measures of Association for Polytomous Variables --- p.Page5 / Chapter §2.1 --- "Notations," --- p.5 / Chapter §2.2 --- "Pearson Product-moment Correlation Coefficient," --- p.6 / Chapter §2.3 --- "Spearman Rank Correlation Coefficient," --- p.7 / Chapter §2.4 --- "Kendall's Tau-b," --- p.9 / Chapter §2.5 --- "Polychoric Correlation Coefficient," --- p.9 / Chapter Chapter 3 --- Monte Carlo Study of Measures of Association for Polytomous Variables with Multivariate Normal Distribution --- p.Page 13 / Chapter §3.1 --- "Design," --- p.13 / Chapter §3.2 --- "Results and Findings," --- p.18 / Chapter §3.3 --- "Discussion," --- p.23 / Chapter §3.4 --- "Implications," --- p.26 / Chapter Chapter 4 --- Monte Carlo Studies for Polytomous Variables with Non-normal Distribution --- p.Page 27 / Chapter §4.1 --- "Elliptica1-t Distribution," --- p.27 / Chapter §4.2 --- "Design," --- p.28 / Chapter §4.3 --- "Results and Findings," --- p.30 / Chapter §4.4 --- "Discussion," --- p.33 / Chapter §4.5 --- "Implications," --- p.34 / Chapter Chapter 5 --- Conclusion --- p.Page36 / References --- p.Page40 / Figures --- p.Page43 / Tables --- p.Page51

by King-hong Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 110-111). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Prediction Problem of Factor Scores --- p.5 / Chapter 2.1 --- The Basic Model --- p.5 / Chapter 2.2 --- Regression Formula in Predicting Factor Scores --- p.7 / Chapter 2.3 --- The Model with Polytomous Variables --- p.9 / Chapter Chapter 3 --- Prediction Methods of Factor Scores --- p.11 / Chapter 3.1 --- Model with Continuous and Polytomous Variables --- p.11 / Chapter 3.2 --- Model with Polytomous Variables --- p.16 / Chapter Chapter 4 --- Monte-Carlo Study --- p.20 / Chapter 4.1 --- Model with Continuous and Polytomous Variables --- p.20 / Chapter 4.1.1 --- Design of the Monte-Carlo Study --- p.20 / Chapter 4.1.2 --- Results of the Monte-Carlo Study --- p.24 / Chapter 4.2 --- Model with Polytomous Variables --- p.30 / Chapter 4.2.1 --- Design of the Monte-Carlo Study --- p.30 / Chapter 4.2.2 --- Results of the Monte-Carlo Study --- p.33 / Chapter Chapter 5 --- Summary and Conclusion --- p.38 / Tables --- p.41 / Figures --- p.56 / References --- p.110

本论文主要研究两类风险估计问题：一类是美式期权价格关于模型参数的敏感性估计， 另一类是投资组合的风险估计。针对这两类问题，我们相应地提出了高效的蒙特卡洛模拟方法。这构成了本文的两个主要部分。 / 第二章是本文的第一部分。在这章中，我们将美式期权的敏感性估计问题提成了更具一般性的估计问题：如果一个随机最优化问题依赖于某些模型参数， 我们该如何估计其最优目标函数关于参数的敏感性。在该问题中， 由于最优决策关于模型参数可能不连续，传统的无穷小扰动分析方法不能直接应用。针对这个困难，我们提出了一种广义的无穷小扰动分析方法，得到敏感性的无偏估计。 我们的方法显示, 在估计敏感性时， 其实并不需要样本路径关于参数的可微性。这是我们在理论上的新发现。另一方面， 该方法可以非常容易的应用于美式期权的敏感性估计。在实际应用中敏感性的无偏估计可以直接嵌入流行的美式期权定价算法，从而同时得到期权价格和价格关于模型参数的敏感性。包括高维问题和多种不同的随机过程模型在内的数值实验， 均显示该估计在计算上具有显著的优越性。最后，我们还从理论上刻画了美式期权的近似最优执行策略对敏感性估计的影响，给出了误差上界。 / 第三章是本文的第二部分。在本章中，我们研究投资组合的风险估计问题。该问题也可被推广成一个一般性的估计问题：如何估计条件期望在作用上一个非线性泛函之后的期望。针对该类估计问题，我们提出了一种多层模拟方法。我们的估计量实际上是一些简单嵌套估计量的线性组合。我们的方法非常容易实现，并且可以被广泛应用于不同的问题结构。理论分析表明我们的方法适用于不同维度的问题并且算法复杂性低于文献中现有的方法。包括低维和高维的数值实验验证了我们的理论分析。 / This dissertation mainly consists of two parts: a generalized infinitesimal perturbation analysis (IPA) approach for American option sensitivities estimation and a multilevel Monte Carlo simulation approach for portfolio risk estimation. / In the first part, we develop efficient Monte Carlo methods for estimating American option sensitivities. The problem can be re-formulated as how to perform sensitivity analysis for a stochastic optimization problem when it has model uncertainty. We introduce a generalized IPA approach to resolve the difficulty caused by discontinuity of the optimal decision with respect to the underlying parameter. The unbiased price-sensitivity estimators yielded from this approach demonstrate significant advantages numerically in both high dimensional environments and various process settings. We can easily embed them into many of the most popular pricing algorithms without extra simulation effort to obtain sensitivities as a by-product of the option price. This generalized approach also casts new insights on how to perform sensitivity analysis using IPA: we do not need pathwise differentiability to apply it. Another contribution of this chapter is to investigate how the estimation quality of sensitivities will be affected by the quality of approximated exercise times. / In the second part, we propose a multilevel nested simulation approach to estimate the expectation of a nonlinear function of a conditional expectation, which has a direct application in portfolio risk estimation problems under various risk measures. Our estimator consists of a linear combination of several standard nested estimators. It is very simple to implement and universally applicable across various problem settings. The results of theoretical analysis show that the algorithmic complexities of our estimators are independent of the problem dimensionality and are better than other alternatives in the literature. Numerical experiments, in both low and high dimensional settings, verify our theoretical analysis. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Liu, Yanchu. / "December 2012." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 89-96). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Abstract in Chinese --- p.iii / Acknowledgements --- p.v / Contents --- p.vii / List of Tables --- p.ix / List of Figures --- p.xii / Chapter 1. --- Overview --- p.1 / Chapter 2. --- American Option Sensitivities Estimation via a Generalized IPA Approach --- p.4 / Chapter 2.1. --- Introduction --- p.4 / Chapter 2.2. --- Formulation of the American Option Pricing Problem --- p.10 / Chapter 2.3. --- Main Results --- p.14 / Chapter 2.3.1. --- A Generalized IPA Approach in the Presence of a Decision Variable --- p.16 / Chapter 2.3.2. --- Unbiased First-Order Sensitivity Estimators --- p.21 / Chapter 2.4. --- Implementation Issues and Error Analysis --- p.23 / Chapter 2.5. --- Numerical Results --- p.26 / Chapter 2.5.1. --- Effects of Dimensionality --- p.27 / Chapter 2.5.2. --- Performance under Various Underlying Processes --- p.29 / Chapter 2.5.3. --- Effects of Exercising Policies --- p.31 / Chapter 2.6. --- Conclusion Remarks and Future Work --- p.33 / Chapter 2.7. --- Appendix --- p.35 / Chapter 2.7.1. --- Proofs of the Main Results --- p.35 / Chapter 2.7.2. --- Likelihood Ratio Estimators --- p.43 / Chapter 2.7.3. --- Derivation of Example 2.3 --- p.49 / Chapter 3. --- Multilevel Monte Carlo Nested Simulation for Risk Estimation --- p.52 / Chapter 3.1. --- Introduction --- p.52 / Chapter 3.1.1. --- Examples --- p.53 / Risk Measurement of Financial Portfolios --- p.53 / Derivatives Pricing --- p.55 / Partial Expected Value of Perfect Information --- p.56 / Chapter 3.1.2. --- A Standard Nested Estimator --- p.57 / Chapter 3.1.3. --- Literature Review --- p.59 / Chapter 3.1.4. --- Summary of Our Contributions --- p.61 / Chapter 3.2. --- The Multilevel Approach --- p.63 / Chapter 3.2.1. --- Motivation --- p.63 / Chapter 3.2.2. --- Multilevel Construction --- p.65 / Chapter 3.2.3. --- Theoretical Analysis --- p.67 / Chapter 3.2.4. --- Further Improvement by Extrapolation --- p.69 / Chapter 3.3. --- Numerical Experiments --- p.72 / Chapter 3.3.1. --- Single Asset Setting --- p.73 / Chapter 3.3.2. --- Multiple Asset Setting --- p.74 / Chapter 3.4. --- Concluding Remarks --- p.77 / Chapter 3.5. --- Appendix: Technical Assumptions and Proofs of the Main Results --- p.79 / Bibliography --- p.89

The ordering processes of ferroelectric and multiferroic materials were investigated via neutron total scattering and the reverse Monte Carlo method. The results presented in this thesis are from three materials where ferroelectric behaviour is a result of ordering of molecular groups rather than individual atoms. Two of the materials are metal-organic frameworks, three dimensional cage-like structures with guest ions inside the pores; the third material, is a room temperature ferroelectric. In the high-temperature phase of dimethylammonium manganese formate, the framework distorts around the disordered cation, and the cations form shorter hydrogen bonds with the formate framework than the average structure suggests. Framework deformations became increasingly unfavourable as the material cooled. The cations continue to order as the material was cooled below Tc. Analysis of the high-temperature phase atomistic configurations showed that in addition to the three known orientations about the threefold axis, a significant minority of the cations lie mid-way between these positions, a feature which could not have been observed via standard crystallographic techniques. The mechanisms for thermal expansion of potassium imidazolium hexacyanoferrate change between the intermediate-temperature phase and the high-temperature phase. In the hightemperature phase the framework distorts around the disordered guest, but in the intermediatetemperature phase the framework stiffens. I propose that the temperature of the dielectric transition is dependent of the volume inside the framework, but that the temperature range of the intermediate-temperature phase is dependent on the rate of contraction of the framework around the guest cation. For triglycine sulfate no correlation was observed between the orientation of the polar molecules and the motion of the intermediate deuterium. Furthermore, in the high temperature phase the atomistic configurations produced models with macroscopic polarisation. I propose that this material forms domains of aligned polar molecules above Tc and that these domains are larger than the atomistic configurations.

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As for the Monte Carlo Method, we first introduce a brief history of the method and pricing options by using the method. Secondly, the basic idea of using the method in computing option price is described. Thirdly, pricing vanilla options is introduced. Fourthly, we discuss some techniques of improving computing accuracy. They include antithetic variables, control variate methods and importance sampling. / Fifth, we study in detail pricing option problems by using the Monte Carlo method. Then we present a new method on pricing American option, by which, the required memory in computation can be significantly reduced. For most methods of pricing American options, bias exists. However, by using the memory reduction method, minimizing biases is possible. We also discuss the problem for valuation of multiasset options by using our method. In fact, this is an important application of the Monte Carlo method in practical financial problems. / Finally, comparisons of the performances of these numerical results are presented. / Some basic concepts on options are first introduced. Then general methods for pricing options are described. These methods include: analytical formula, finite difference methods and binomial and multinomial methods. These prepare us for the in-depth study on the Monte Carlo method in subsequent chapters. / The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. The Monte Carlo method is the main topic of the thesis. / by Chen Yong. / "August 2002." / Adviser: Raymond Chan. / Source: Dissertation Abstracts International, Volume: 63-10, Section: B, page: 4710. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 77-79). / 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.