Stochastic volatility models have long provided a popular alternative to the Black- Scholes-Merton framework. They provide, in a self-consistent way, an explanation for the presence of implied volatility smiles/skews seen in practice. Incorporating jumps into the stochastic volatility framework gives further freedom to nancial mathematicians to t both the short and long end of the implied volatility surface. We present three stochastic volatility models here - the Heston model, the Bates model and the SVJJ model. The latter two models incorporate jumps in the stock price process and, in the case of the SVJJ model, jumps in the volatility process. We analyse the e ects that the di erent model parameters have on the implied volatility surface as well as the returns distribution. We also present pricing techniques for determining vanilla European option prices under the dynamics of the three models. These include the fast Fourier transform (FFT) framework of Carr and Madan as well as two Monte Carlo pricing methods. Making use of the FFT pricing framework, we present calibration techniques for tting the models to option data. Speci cally, we examine the use of the genetic algorithm, adaptive simulated annealing and a MATLAB optimisation routine for tting the models to option data via a leastsquares calibration routine. We favour the genetic algorithm and make use of it in tting the three models to ALSI and S&P 500 option data. The last section of the dissertation provides hedging techniques for the models via the calculation of option price sensitivities. We nd that a delta, vega and gamma hedging scheme provides the best results for the Heston model. The inclusion of jumps in the stock price and volatility processes, however, worsens the performance of this scheme. MATLAB code for some of the routines implemented is provided in the appendix.

Master of Management in Finance & Investment Faculty of Commerce Law and Management Wits Business School University of The Witwatersrand 2016 / The Value-at-Risk (VaR) measurement – which is a single summary, distribution independent statistical measure of losses arising as a result of market movements – has become the market standard for measuring downside risk. There are some diverse ways to computing VaR and with this diversity comes the problem of determining which methods accurately measure and forecast Value-at-Risk. The problem is two-fold. First, what is the distribution of returns for the underlying asset? When dealing with linear financial instruments – where the relationship between the return on the financial asset and the return on the underlying is linear– we can assume normality of returns. This assumption becomes problematic for non-linear financial instruments such as options. Secondly, there are different methods of measuring the volatility of the underlying asset. These range from the univariate GARCH to the multivariate GARCH models. Recent studies have introduced the Independent Component Analysis (ICA) GARCH methodology which is aimed at computational efficiency for the multivariate GARCH methodologies. In our study, we focus on non-linear financial instruments and contribute to the body of knowledge by determining the optimal combination for the measure for volatility of the underlying (univariate-GARCH, EWMA, ICA-GARCH) and the distributional assumption of returns for the financial instrument (assumption of normality, the Johnson translation system). We use back-testing and out-of-sample tests to validate the performance of each of these combinations which give rise to six different methods for value-at-risk computations. / MT2017

University of Macau / Faculty of Science and Technology. / Department of Computer and Information Science

Advertising is considered as an important strategic tool to promote product and improve sales. Extensive research has been devoted to advertising strategies and their effect on product sales. Chiefly because aggregate-level sales data are easy to collect, the prior studies predominately develop and analyze aggregate advertising models which relate product sales to advertising spending under a known sales response function. Nowadays, however, the emergence of Internet, e-commerce and data analytics approaches has made collecting data on individual consumer behavior and real-time sales feasible. Therefore, studying more sophisticated advertising models which can exploit these data is necessary and meaningful. In this dissertation, we consider two dynamic advertising models, one incorporates customer satisfaction and customer switching behavior and the other involves dynamic sales learning. / The first model focuses on the markets of experience goods whose quality levels are unobservable to the buyers. The buyers make the purchase decisions based on their past usage experience of the goods and the advertising outlays of the sellers. We first consider the competitive market where there are multiple brands planning their advertising campaigns. We derive the long-term steady-state equilibrium advertising strategies and market shares of the brands. We study how customer reaction to their past usage experience of the product (satisfaction) affects the sellers’ advertising strategies and market shares. We further analyze the monopoly market, where the focus is on the question of whether the monopolist should use even-level advertising or pulsing advertising strategy. / In the second model, we study the dynamic advertising budget allocation problems, in which the relationship between the advertising expenditure and the product sales is unknown to the retailer and the retailer can only learn this information through observing realized sales. We propose nonparametric advertising budget allocation policies for both single- and multi-product problems. We show that such policies are asymptotically optimal. In particular, for the single-product problem, by constructing a lower-bound instance, we show that our policy achieves near-best asymptotic performance. / 广告预算的确定和分配是企业运营中一个极为重要的决策。而广告资金的动态支出策略已经被研究了数十年。由于以前可获取的数据往往仅限于市场的一些宏观数据。传统文献主要用一个已知的销售响应函数从宏观层面刻画广告支出和销售量之间的关系。现今，随着互联网，电子商务，社交媒体和数据分析方法的出现，使收集有关消费者行为和实时销售量的数据成为可能。合理地利用这些数据可以大大提高企业的广告效率。这也给广告策略的研究带来了新的契机。本论文研究两个动态广告支出策略模型，一个模型涉及顾客满意度和顾客转换行为，另外一个涉及销售响应函数的动态学习。 / 本文的第一个模型考虑体验商品市场中卖家的广告支出策略。在市场中，顾客没有办法观测到产品的真实质量，他们的产品选择受到自己之前的产品体验和卖家的广告支出的影响。我们首先考虑有竞争的市场，市场中有多个品牌同时进行广告支出决策。我们推导了市场的长期稳态平衡。研究了不同的客户满意度与顾客转换行为的关系对卖家的广告支出策略和市场份额的影响。然后，我们分析了垄断市场中垄断卖家的长期广告支出策略。此外，我们还讨论了该卖家应该使用持续的广告投入策略还是周期性脉冲广告策略的问题。 / 本文的第二个模型研究是的动态广告预算分配问题。我们假设卖家起初并不知道广告支出的销售响应函数，他只能通过观察实时销售数据来对销售响应函数进行学习。我们分别考虑了单产品和多产品的问题，并提出了相应的非参数动态广告预算分配策略。我们证明了所提出的动态预算分配策略是渐进最优的。对于单产品的问题，通过构造出一类“最坏”的响应函数，我们证明了所提出的动态预算分配策略的渐进绩效已基本接近最优。 / Yang, Chaolin. / Thesis Ph.D. Chinese University of Hong Kong 2015. / Includes bibliographical references (leaves 133-140). / Abstracts also in Chinese. / Title from PDF title page (viewed on 12, October, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.

Lim Sze Wah. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 71-73). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- A brief review on the basic minority game --- p.6 / Chapter 2.1 --- Model --- p.7 / Chapter 2.2 --- Results --- p.9 / Chapter 2.3 --- Discussion --- p.11 / Chapter 2.3.1 --- Bit-string Statistics and Market Efficiency --- p.11 / Chapter 2.3.2 --- Crowds and Anticrowds Effect --- p.14 / Chapter 2.3.3 --- Hamming Distance and Reduced Strategies Space --- p.15 / Chapter 3 --- A brief review on existing variations on the minority game --- p.17 / Chapter 3.1 --- Darwinism process and MG --- p.17 / Chapter 3.2 --- Evolutionary MG (EMG) --- p.17 / Chapter 3.3 --- Modified EMG (MEMG) --- p.18 / Chapter 3.4 --- MG with arbitrary cutoff --- p.18 / Chapter 3.5 --- Thermal MG (TMG) --- p.19 / Chapter 3.6 --- Three-Sided MG --- p.19 / Chapter 3.7 --- MG with variable payoffs --- p.19 / Chapter 4 --- Minority game with varying number of participants --- p.21 / Chapter 4.1 --- The modified MG --- p.22 / Chapter 4.1.1 --- Model --- p.22 / Chapter 4.1.2 --- Results --- p.23 / Chapter 4.2 --- Mixed-population --- p.33 / Chapter 4.2.1 --- Model --- p.33 / Chapter 4.2.2 --- Results --- p.33 / Chapter 4.2.3 --- Discussions --- p.37 / Chapter 5 --- Minority game considering recent performance of strategies --- p.39 / Chapter 5.1 --- The modified MG --- p.40 / Chapter 5.1.1 --- Model --- p.40 / Chapter 5.1.2 --- Results --- p.40 / Chapter 5.2 --- Mixed-population --- p.46 / Chapter 5.2.1 --- Model --- p.46 / Chapter 5.2.2 --- Results --- p.47 / Chapter 5.2.3 --- Discussions --- p.50 / Chapter 6 --- Minority game combining both modifications --- p.52 / Chapter 6.1 --- Model --- p.52 / Chapter 6.2 --- Results --- p.53 / Chapter 7 --- Conclusion --- p.68 / Bibliography --- p.71

Leong Chan Fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 100-105). / Abstracts in English and Chinese. / Abstract --- p.i-ii / Acknowledgements --- p.iii / Table of Contents --- p.iv / List of Tables --- p.v / List of Figures --- p.vi / Chapter Section 1 --- Introduction --- p.1 / Chapter Section 2 --- Literature Review --- p.5 / Chapter Section 3 --- Data Description --- p.13 / Chapter 3.1 --- Transaction Prices --- p.13 / Chapter 3.2 --- Macroeconomic Variables --- p.15 / Chapter Section 4 --- Methodology --- p.19 / Chapter 4.1 --- Hedonic Pricing --- p.21 / Chapter 4.2 --- Measurements --- p.22 / Chapter 4.3 --- Stationarity --- p.24 / Chapter 4.4 --- Vector Autoregressive Model and Granger Causality --- p.27 / Chapter Section 5 --- Hypothesis Testing --- p.31 / Chapter Section 6 --- Empirical Results --- p.35 / Chapter 6.1 --- Hedonic Pricing Models --- p.35 / Chapter 6.2 --- Real Housing Price Dispersion Indicators and Macro Variables --- p.36 / Chapter 6.3 --- Stationary Tests --- p.37 / Chapter 6.4 --- Results from the Ordinary Least Square Regressions --- p.37 / Chapter 6.5 --- Results from the Vector Auto Regressive Models --- p.40 / Summary and Conclusion --- p.46 / Appendix 1 Tables --- p.49 / Appendix 2 Figures --- p.80 / Reference --- p.100

In this thesis, we mainly study the portfolio selection problem with a set of index and options of stocks, based on a refined mean-variance methodology. Models in single-stage and multistage cases are studied, with a formulation using a scenario tree structure. We first investigate the pattern of the payoff of the optimal optioned portfolio. It turns out there is a rich structure with many interesting properties, including the piecewise linearity, risk-free return at some fixed scenarios, etc. We then extend the model to accommodate the features of multistage formulations. Both the mathematical programming methodology and the stochastic control methodology are applied to solve the decision model based on a scenario tree structure. Analytical formulations of the optimal portfolio together with an expression of the efficient frontier are derived. We also make an analysis of the relations between the two approaches. We further study some variations of the mean-variance formulation. These models are applied to construct a portfolio with same preferred payoff characters, such as monotonic payoff or guaranteed payoff. Finally, the tracking model is considered in this thesis. The optimal payoff and its mean-variance efficiency are analyzed. Throughout the thesis, many numerical examples with real life data are used to illustrate and validate our results. / Liang Jianfeng. / "May 2004." / Source: Dissertation Abstracts International, Volume: 66-01, Section: B, page: 0529. / Supervisors: Duan Li; Shuzhong Zhang. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 120-126). / Available also through the Internet via Current research @ Chinese University of Hong Kong under title: Optioned portfolio selection models, analysis, and solution methods / 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. / Abstracts in English and Chinese. / School code: 1307.

About the intraday volatility modeling, the limitations and potential problems of using Andersen & Bollerslev's approach are addressed and distinct modifications are proposed to tackle the corresponding issues. The first suggestion is about the utilization of the interaction between the intraday periodicity and the heteroskedasticity while the second is about the modified normalization for the estimation of the intraday periodicity. / Furthermore, it is demonstrated that the inclusion of overnight variance can improve the prediction accuracy of the Chicago Board of options Exchange (CBOE) volatility indexes (VIX and VXD) under specific weight combinations. The findings contradict the common perception that overnight return does not contain useful information for daily volatility modeling. / On the other hand, the third suggestion is about the inclusion of overnight information for the estimation of daily volatility. This study explores the possibility of incorporating the overnight variance indirectly through the use of linearly combined daily volatility estimators. The empirical results demonstrate that the inclusion of overnight variance can produce substantial influence when the minimum-variance constraints are relaxed. Besides, the influence is revealed to be not monotonic as an increase of the overnight proportion does not necessarily produce a larger influence. / The proposed modifications are tested with different ARCH structures, including GARCH(1,1), FIGARCH(1,d,1) and HYGARCH(1,d,1), by using simulated data and market data. Apart from studying the 1-step-ahead out-of-sample performance, several multiple-step-ahead forecasting results are also addressed. Under the same level of model flexibility (parameterized portions), our proposed modifications always outperform the original method in both in-sample fitness and out-of-sample performance on various forecasting horizons. / This research study investigates three new considerations for improving the performance of volatility modeling of financial returns. Two of them are related to the intraday volatility modeling and the other one is about the use of overnight information for daily volatility modeling. / Chu, Chun Fai Carlin. / Adviser: Kai Pui Lam. / Source: Dissertation Abstracts International, Volume: 73-04, Section: A, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 180-186). / 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 Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Another achievement of this research is to elaborate the modified concept of Cash Rebate Mortgages. To examine the difference between Cash Rebate Mortgages and standard mortgages, we have built a simulation model to study the behavior of these two types of mortgages. The results indicate that the value of Cash Rebate Mortgages is higher than that of standard mortgages, but is more sensitive to embedded options. If the probability of exercising an option is higher, then the value of Cash Rebate Mortgages will drop at a faster rate than that of standard mortgages. / Several findings are elaborated in this dissertation. Our model has identified the major contributors to mortgage prepayment, and has developed a logistic regression model to describe prepayment behavior. We further illustrate that prepayment and default behavior are associated with financial reasons: the value of the refinancing incentive is usually greater than the prepayment penalty plus the transaction cost for refinancing mortgages, and the outstanding balance of the mortgage is higher than the current market value of the underlying property minus the transaction cost. / The final objective of this dissertation is to develop an option model for MBS issuers. Most previous studies that have developed MBS models have focused on investors, but the model that is presented here is specifically for MBS issuers. The current study develops a risk management tool for issuers and guarantors to monitor their MBS portfolios. The model projects the cash inflow of mortgages and the cash outflow to MBS, alters the traditional model by introducing decision trees, and uses a simulation program with multiple path generation to develop a model for issuers to manage their MBS portfolios. According to the results of the model, issuers can manage the risk level of their portfolios by determining the Collection Account Balance, the Overcollateralization Ratio, the Net Residual Value, and the Liquidity Advance. Finally this paper also provides suggestions on risk management for MBS issuers. / The objective of this dissertation is to develop an option model for residential mortgages and Mortgage-Backed Securities. Previous studies in the literature have identified several research opportunities that have not yet been explored. The current study attempts to fill the research gap, by altering the traditional model of mortgage valuation with a trinomial tree. We combine the prepayment, delinquency, default, and recovery of delinquency into a single model, to build a simulation program to generate different cash flow scenarios. The industrial data of the Korea Mortgage Corporation and a medium sized Hong Kong bank are used as empirical evidence for the model. / by Yat-ming Lam. / "February 2003." / Source: Dissertation Abstracts International, Volume: 64-09, Section: A, page: 3408. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. [222-235]). / Available also through the Internet via Current research @ Chinese University of Hong Kong under title: Option theory for mortgages and mortgage-backed securities (Korea, China) / 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. / School code: 1307.

Zhou Xiaozhou. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 58-59). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview --- p.1 / Chapter 1.2 --- Organization Outline --- p.4 / Chapter 2 --- Literature Review --- p.5 / Chapter 2.1 --- Option --- p.5 / Chapter 2.1.1 --- The definition of option --- p.5 / Chapter 2.1.2 --- Payoff of Options --- p.6 / Chapter 2.1.3 --- Black-Scholes Option Pricing Model --- p.7 / Chapter 2.1.4 --- Binomial Model --- p.12 / Chapter 2.2 --- Portfolio Theory --- p.15 / Chapter 2.2.1 --- The Markowitz Mean-Variance Model --- p.15 / Chapter 2.2.2 --- Multi-period Mean-Variance Formulation --- p.17 / Chapter 3 --- Multi-Period Options Portfolio Selection Model with Guaran- teed Return --- p.20 / Chapter 3.1 --- Problem Formulation --- p.20 / Chapter 3.2 --- Solution Algorithm Using Dynamic Programming --- p.25 / Chapter 3.3 --- Numerical Example --- p.27 / Chapter 4 --- Mean-Variance Formulation of Options Portfolio --- p.36 / Chapter 4.1 --- The Problem Formulation --- p.36 / Chapter 4.2 --- Solution Algorithm Using Dynamic Programming --- p.39 / Chapter 4.3 --- Numerical Example --- p.41 / Chapter 5 --- Summary --- p.56