The project investigates the prices of barrier options from the constant underlying volatility in the Black-Scholes model to stochastic volatility model in SABR framework. The constant volatility assumption in derivative pricing is not able to capture the dynamics of volatility. In order to resolve the shortcomings of the Black-Scholes model, it becomes necessary to find a model that reproduces the smile effect of the volatility. To model the volatility more accurately, we look into the recently developed SABR model which is widely used by practitioners in the financial industry. Pricing a barrier option whose payoff to be path dependent intrigued us to find a proper numerical method to approximate its price. We discuss the basic sampling methods of Monte Carlo and several popular variance reduction techniques. Then, we apply Monte Carlo methods to simulate the price of the down-and-out put barrier options under the Black-Scholes model and the SABR model as well as compare the features of these two models.

There is a growing global need for proper access to radiation therapy. This need exists predominantly in low- and middle-income countries but exists in some high-income countries as well. The solution to this problem is complex and requires changes in government policy, education and technology. The objective of the work contained in this dissertation is the development of a novel external beam radiation therapy system capable of treating a variety of cancers. The intent of this system is to provide a cost-effective radiation therapy system, which can primarily be utilized in low- and middle-income countries. This new system uses kilovoltage rather than megavoltage x-rays and is therefore much more cost-effective. The ultimate purpose of this kilovoltage radiation therapy system is to improve access to radiation therapy worldwide by supplementing current radiation therapy technology. As a first step, the kilovoltage x-ray arc therapy or KVAT system was modeled using the EGSnrc BEAMnrc and DOSXYZnrc Monte Carlo software tools. For this initial study 200 kV arc-therapy was simulated on cylindrical water phantoms of two sizes, each of which contained a variety of planning target volume (PTV) sizes and locations. Additionally, prone and supine partial breast irradiation treatment plans were generated using KVAT. The objective of this work was to determine whether or not skin-sparing could be achieved using the KVAT system while also delivering a clinically relevant dose rate to the PTV. The results of the study indicated that skin-sparing is indeed achievable and that the quality of KVAT treatment plans improves for full 360-degree arcs and smaller PTV sizes. The second step of this project involved the Monte Carlo simulation of KVAT treatment plans for breast, lung and prostate cancer. Spherical PTVs of 3-cm diameter were used for the breast and lung treatment plans while a 4-cm diameter PTV was used for prostate. Additionally, inverse optimization was utilized to make full use of the non-conformal irradiation geometry of KVAT. As a means of comparison, megavoltage treatment plans that could be delivered by a clinical linear accelerator were generated for each patient as well. In order to evaluate the safety of KVAT treatment plans, dose constraints were taken from published Radiation Therapy Oncology Group (RTOG) reports. The results of this study indicated that the 200 kV breast and 225 kV lung KVAT treatment plans were within dose constraints and could be delivered in a reasonable length of time. The 225 kV prostate treatment plan, while technically within dose constraints, delivered a large dose to non-critical healthy tissues due to the limited number of beam angles that did not pass through boney anatomy. It was concluded that plans such as prostate with large volumes of bone present might not be feasible for KVAT treatment. The third step aimed to expand upon previous work and simulated more realistic KVAT treatment plans by using PTV volumes contoured by radiation oncologists. Additionally, this study used a completely redesigned KVAT geometry, which employed a stationary reflection anode and a new collimator design. The design modeled in this study was based upon the specifications of the prototype system under construction by PrecisionRT, a commercial partner. Three stereotactic ablative radiotherapy (SABR) lung patients were selected that had received treatment at the Vancouver Island Cancer Centre. In order to fully cover the PTVs of each patient, spherical sub-volumes were placed within the clinically contoured PTV of each patient. Dose constraints for at-risk organs were taken from an RTOG report on stereotactic body radiation therapy and were used to inversely optimize the 200 kV KVAT treatment plans. The calculated KVAT plans were compared with the clinical 6 MV SABR plans delivered to each patient. The results of this study indicated that KVAT lung plans were within dose constraints for all three patients with the exception of the ribs in the second patient who had a tumor directly adjacent to the rib cage. The fourth and last step of this project was the experimental validation of a simple, proof-of-principle KVAT system. Simple geometric methods were used to design a collimator consisting of two slabs of brass separated by ~6 cm, each with 5 apertures, which would create an array of 5 converging beamlets. The collimator was used with a tabletop x-ray tube system. A rectangular solid water phantom and cylindrical TIVAR 1000 phantom were placed on a rotation stage and irradiated using 360-degree arcs. EBT3 gafchromic film was placed in each phantom to measure two-dimensional dose distributions. Film dose distributions were analyzed and compared to Monte Carlo generated dose distributions. Both the rectangular solid water phantom and cylindrical TIVAR phantom showed skin-sparing effects in their dose distributions. The highest degree of skin-sparing was achieved in the larger, 20 cm diameter cylindrical phantom. Furthermore, the measured film data and calculated metrics of the rectangular phantom were within 10% of the MC calculated values for two out of three films. The discrepancy in the third film can be explained by errors in the experimental setup. In conclusion, the work contained in this dissertation has established the feasibility of a cost-effective kilovoltage arc-therapy system designed to treat deep-seated lesions by means of Monte Carlo simulations and experimental dosimetry. The studies performed so far suggest that KVAT is most suitable for smaller lesions in patient anatomy that does not involve large amounts of boney anatomy. Perhaps most importantly, an experimental study has demonstrated the skin-sparing ability of a simple KVAT prototype. / Graduate / 2020-07-10

Nesse trabalho investigamos através de simulações numéricas a evolução da composição genética de uma população, dando atenção especial ao processo dinâmico conhecido como catraca de Muller, que é responsável pela degradação da população devido ao acúmulo de mutações deletérias em populações finitas. Consideramos também a genealogia dos indivíduos em uma população sob a ação da catraca de Muller. Ainda, investigamos analiticamente o limite determinístico do modelo, no qual o tamanho da população é infinito, onde o processo da catraca não atua. O relevo replicativo, ou seja, a função que mapeia a carga genética de um indivíduo com a sua probabilidade de reprodução utilizado nesse trabalho é uma generalização do relevo originalmente proposto por Muller para ilustrar o processo da catraca. Adicionamos a esse relevo um parâmetro de epistase que simula a interação entre os sítios das seqüências dos indivíduos. A escolha desse parâmetro determina três tipos possíveis de epistase: (i) sinergística, no qual as mutações ficam cada vez mais deletérias com o número de mutações já existentes; (ii) atenuante, no qual o efeito deletério de uma nova mutação é atenuado; e (iii) multiplicativa, no qual as novas mutações causam danos idênticos, independentemente do número anterior de mutações / In this work we investigate through numerical simulations the evolution of the genetic composition of a population, giving emphasis to the dynamic process termed Muller\'s ratchet, which is responsible for the degradation of the population due to the accumulation of deleterious mutations in finite populations. We consider also the genealogy of the individuals evolving in a population under the effect of the Muller\'s ratchet. In addition, we investigate analytically the deterministic limit of the model, in which the population size is infinite, where ratchet process does not act. The replication landscape, i.e., the function that maps the genetic load of an individual on its probability of reproduction used in this work is a generalization of that originally considered by Muller to illustrate the process of the ratchet. In particular, we add to that landscape a parameter of epistasis that models the interactions among the sites of the sequences of the individuals. The tunning of this parameter determines three different types of epistasis: (i) synergistic, where the mutations become more deleterious with the number of mutations already present; (ii) diminishing, where the deleterious effect of a new mutation is attenuated; and (iii) multiplicative, where the new mutations cause identical damages, independently of the previous number of mutations

Nas reações de pré-equilíbrio os modelos de exciton de Griggin e Hibrido de Blann mostraram bastante sucesso em descrever a dependência energética e, até certo ponto a depêndencia ângular, na emissão de nucleons e emissão de partículas compostas. No entanto a base conceitual desses modelos foi questionada por Bisplinghoff há algum tempo. Cálculos numéricos corroboram com suas dúvidas. Em resposta a Bisplinghoff, Blann propôs o modelo Hybrid Monte Carlo (HMS), que utiliza somente as densidades de estados disponíveis para a criação e aniquilação de pares partículas-buracos. O modelo foi posteriormente estendido, em colaboração com Chadwick, ao Double Differential Hybrid Monte Carlo (DDHMS). Esta extensão é baseada na aproximação de Chadwick e Oblozinský da distribuição angular e de energia dos estados de duas partículas e um buraco disponíveis e que leva em conta a conservação do momento. Este trabalho faz uma comparação com a distribuição energética e angular exatas relativísticas e não relativísticas. E dos espectros de emissão acessíveis de prótons produzidos pelo código EMPIRE, que é um sistema modular de códigos de reações nucleares, compreendendo vários modelos nucleares, e que premite realizar cálculos com um grande números de partículas e energias. Em particular utilizamos o modúlo do modelo Double Differential Hybrid Monte Carlo que realiza cálculos Monte Carlo de emissão utilizando densidades de transição com base no modelo de exciton, nos modelos aproximados e exatos de um gás de Fermi.

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