Guo, Min. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 66-69). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Notation and Model --- p.8 / Chapter 2.1 --- Notation --- p.9 / Chapter 2.2 --- Classical News vendor Model --- p.11 / Chapter 2.3 --- The Price of the Put Option --- p.12 / Chapter 2.4 --- Extended Models with the Option --- p.13 / Chapter 3 --- Literature Review --- p.16 / Chapter 4 --- Objective I ´ؤ Maximizing Expected Profit --- p.24 / Chapter 4.1 --- Single Decision Variable Case: K = Q --- p.24 / Chapter 4.2 --- Two Decision Variable Case: K ≤Q --- p.25 / Chapter 4.3 --- Summary of the Chapter --- p.28 / Chapter 5 --- Objective II ´ؤ Maximizing the Probability of Achieving A Target Profit --- p.30 / Chapter 5.1 --- Single Decision Variable Case: K = Q --- p.30 / Chapter 5.2 --- Two Decision Variable Case: K ≤ Q --- p.37 / Chapter 5.3 --- Numerical Examples --- p.38 / Chapter 5.4 --- Summary of the Chapter --- p.41 / Chapter 6 --- Objective III ´ؤ Minimizing Profit Variance --- p.43 / Chapter 6.1 --- Minimizing Profit Variance through R --- p.44 / Chapter 6.2 --- Minimizing Profit Variance through K --- p.51 / Chapter 6.2.1 --- Special Case R = s --- p.54 / Chapter 6.3 --- Summary of the Chapter --- p.60 / Chapter 7 --- Conclusion --- p.63 / Bibliography --- p.69

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.

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

He, Huifen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 44-48). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Literature Review --- p.4 / Chapter 1.2.1 --- Supply Contracts under Price Uncertainty --- p.5 / Chapter 1.2.2 --- Dual Sourcing --- p.6 / Chapter 1.2.3 --- Risk Aversion in Inventory Management --- p.6 / Chapter 1.2.4 --- Hedging Operational Risk Using Financial Instruments --- p.7 / Chapter 1.2.5 --- Financial Literature --- p.9 / Chapter 1.3 --- Organization of the Thesis --- p.10 / Chapter 2 --- A Risk-Neutral Model --- p.12 / Chapter 2.1 --- Framework and Assumptions --- p.12 / Chapter 2.2 --- "Price, Forward and Convenience Yield" --- p.14 / Chapter 2.2.1 --- Stochastic Model of Price --- p.14 / Chapter 2.2.2 --- Marginal Convenience Yield --- p.16 / Chapter 2.3 --- Optimality Equations --- p.17 / Chapter 2.4 --- The Structure of the Optimal Policy --- p.21 / Chapter 2.4.1 --- One-period. Optimal Hedge Decision Rule --- p.21 / Chapter 2.4.2 --- One-period Optimal Orderings Decision Rule --- p.23 / Chapter 2.4.3 --- Optimal Policy --- p.24 / Chapter 3 --- A Risk-Averse Model --- p.28 / Chapter 3.1 --- Risk Aversion Modeling and Utility Function --- p.28 / Chapter 3.2 --- Multi-Period Inventory Modelling --- p.31 / Chapter 3.3 --- Exponential Utility Model --- p.33 / Chapter 3.4 --- Optimal Ordering and Hedging Policy for Multi-Period Problem --- p.37 / Chapter 4 --- Conclusion and Future Research --- p.40 / Bibliography --- p.44 / Chapter A --- Appendix --- p.49 / Chapter A.l --- Notation --- p.49 / Chapter A.2 --- K-Concavity --- p.50

Research conducted in mathematical finance focuses on the quantitative modeling of financial markets. It allows one to solve financial problems by using mathematical methods and provides understanding and prediction of the complicated financial behaviors. In this thesis, efforts are devoted to derive and extend stochastic optimization models in financial economics and establish practical algorithms for representing and solving problems in mathematical finance. An option gives the holder the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before a specified date. In this thesis, a valuation model for a perpetual convertible bond is developed when the price dynamics of the underlying share are governed by Markovian regime-switching models. By making use of the relationship between the convertible bond and an American option, the valuation of a perpetual convertible bond can be transformed into an optimal stopping problem. A novel approach is also proposed to discuss an optimal inventory level of a retail product from a real option perspective in this thesis. The expected present value of the net profit from selling the product which is the objective function of the optimal inventory problem can be given by the actuarial value of a real option. Hence, option pricing techniques are adopted to solve the optimal inventory problem in this thesis. The goal of risk management is to eliminate or minimize the level of risk associated with a business operation. In the risk measurement literature, there is relatively little amount of work focusing on the risk measurement and management of interest rate instruments. This thesis concerns about building a risk measurement framework based on some modern risk measures, such as Value-at-Risk (VaR) and Expected Shortfall (ES), for describing and quantifying the risk of interest rate sensitive instruments. From the lessons of the recent financial turmoils, it is understood that maximizing profits is not the only objective that needs to be taken into account. The consideration for risk control is of primal importance. Hence, an optimal submission problem of bid and ask quotes in the presence of risk constraints is studied in this thesis. The optimal submission problem of bid and ask quotes is formulated as a stochastic optimal control problem. Portfolio management is a professional management of various securities and assets in order to match investment objectives and balance risk against performance. Different choices of time series models for asset price may lead to different portfolio management strategies. In this thesis, a discrete-time dynamic programming approach which is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system is explored. It’s also interesting to analyze the implications of the heteroscedastic effect described by a continuous-time stochastic volatility model for evaluating risk of a cash management problem. In this thesis, a continuous-time dynamic programming approach is employed to investigate the cash management problem under stochastic volatility model and constant volatility model respectively. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Although options have been traded for many centuries, it has remained a relatively thinly traded financial instrument. Paradoxically, the theory of option pricing has been studied extensively. This is due to the fact that many of the financial instruments that are traded in the market place have an option-like structure, and thus the development of a methodology for option-pricing may lead to a general methodology for the pricing of these derivative-assets. This thesis will focus on the development of the theory of option pricing. Initially, a fundamental principle that underlies the theory of option valuation will be given. This will be followed by a discussion of the different types of option pricing models that are prevalent in the literature. Special attention will then be given to a detailed derivation of both the Black-Scholes and the Binomial Option pricing models, which will be followed by a proof of the convergence of the Binomial pricing model to the Black-Scholes model. The Black-Scholes model will be adapted to take into account the payment of dividends, the possibility of a changing inter est rate and the possibility of a stochastic variance for the rate of return on the underlying as set. Several applications of the Black-Scholes model will finally be presented. / Thesis (M.Sc.)-University of Natal, 1992.

This thesis studies the problems of semistatic trading strategies in a discrete-time financial market, where stocks are traded dynamically and European options at maturity are traded statically. First, we show that pointwise limits of semistatic trading strategies are again semistatic strategies. The analysis is carried out in full generality for a two-period model, and under a probabilistic condition for multi-period, multi-stock models. Our result contrasts with a counterexample of Acciaio, Larsson and Schachermayer, and shows that their observation is due to a failure of integrability rather than instability of the semistatic form. Mathematically, our results relate to the decomposability of functions as studied in the context of Schrödinger bridges. Second, we study the so-called martingale Schrödinger bridge 𝑄⁎ in a two-period financial market; that is, the minimal-entropy martingale measure among all models calibrated to option prices. This minimization is shown to be in duality with an exponential utility maximization over semistatic portfolios. Under a technical condition on the physical measure 𝑃, we show that an optimal portfolio exists and provides an explicit solution for 𝑄⁎. Specifically, we exhibit a dense subset of calibrated martingale measures with particular properties to show that the portfolio in question has a well-defined and integrable option position.

This thesis contains a discussion of four problems arising from the application of stochastic differential equations and real option theory to investment decision problems in a continuous-time framework. It is based on four papers written jointly with the author’s supervisor. In the first problem, we study an evolutionary stock market model in a continuous-time framework where uncertainty in dividends is produced by a single Wiener process. The model is an adaptation to a continuous-time framework of a discrete evolutionary stock market model developed by Evstigneev, Hens and Schenk-Hoppé (2006). We consider the case of fix-mix strategies and derive the stochastic differential equations which determine the evolution of the wealth processes of the various market players. The wealth dynamics for various initial set-ups of the market are simulated. In the second problem, we apply an entry-exit model in real option theory to study concessionary agreements between a private company and a state government to run a privatised business or project. The private company can choose the time to enter into the agreement and can also choose the time to exit the agreement if the project becomes unprofitable. An early termination of the agreement by the company might mean that it has to pay a penalty fee to the government. Optimal times for the company to enter and exit the agreement are calculated. The dynamics of the project are assumed to follow either a geometric mean reversion process or geometric Brownian motion. A comparative analysis is provided. Particular emphasis is given to the role of uncertainty and how uncertainty affects the average time that the concessionary agreement is active. The effect of uncertainty is studied by using Monte Carlo simulation. In the third problem, we study numerical methods for solving stochastic optimal control problems which are linear in the control. In particular, we investigate methods based on spline functions for solving the two-point boundary value problems that arise from the method of dynamic programming. In the general case, where only the value function and its first derivative are guaranteed to be continuous, piecewise quadratic polynomials are used in the solution. However, under certain conditions, the continuity of the second derivative is also guaranteed. In this case, piecewise cubic polynomials are used in the solution. We show how the computational time and memory requirements of the solution algorithm can be improved by effectively reducing the dimension of the problem. Numerical examples which demonstrate the effectiveness of our method are provided. Lastly, we study the situation where, by partial privatisation, a government gives a private company the opportunity to invest in a government-owned business. After payment of an initial instalment cost, the private company’s investments are assumed to be flexible within a range [0, k] while the investment in the business continues. We model the problem in a real option framework and use a geometric mean reversion process to describe the dynamics of the business. We use the method of dynamic programming to determine the optimal time for the private company to enter and pay the initial instalment cost as well as the optimal dynamic investment strategy that it follows afterwards. Since an analytic solution cannot be obtained for the dynamic programming equations, we use quadratic splines to obtain a numerical solution. Finally we determine the optimal degree of privatisation in our model from the perspective of the government.

巨災權益賣權(CatEPut option) 是種常見的與風險掛鉤的證券(risk-linked security) ，它經常被用來對沖巨災風險，在這篇文章中，我們在隨機利息率和隨機波動率的條件下對巨災權益實權進行定價。我們使用了高維傅利葉變換的方法來進行定價，并得到了巨災權益賈權價格的顯式表達，數據實驗的結果顯示，我們的定價公式和方法是高效和精確的。此外，我們還發現隨機利息率和隨機波動率對巨災權益賣權的價格有很大影響。 / The catastrophic equity put (CatEPut) options which serve as a kind of risklinked securities are quite popular in hedging catastrophic risk. In this thesis, the CatEPut options are priced with the stochastic interest rate and stochastic volatility (SISV). We use a two-dimensional Fourier transform over the log price and the catastrophic loss to derive the closed-form CatEPut option price. The numerical examples show that our pricing formula and method are efficient and accurate. We also find that the price of the CatEPut options are greatly in uenced by the stochastic volatility and stochastic interest rate. / Detailed summary in vernacular field only. / Li, Yiran. / "September 2012." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 54-55). / Abstracts also in Chinese. / Abstract --- p.i / Abstract in Chinese --- p.ii / Acknowledgements --- p.iii / Contents --- p.v / List of Tables --- p.vii / List of Figures --- p.viii / Chapter 1. --- Introduction --- p.1 / Chapter 2. --- The model --- p.5 / Chapter 2.1. --- The model of CatEPut options under risk-neutral measure --- p.5 / Chapter 2.2. --- Change to the forward measure --- p.7 / Chapter 3. --- Pricing CatEPut using “conditioning on the catastrophic lossmethod --- p.10 / Chapter 4. --- Pricing CatEPut using Fourier transform --- p.15 / Chapter 5. --- Numerical experiments --- p.26 / Chapter 5.1 --- The FFT algorithm --- p.26 / Chapter 5.2 --- The impact of the stochastic interest rate and the stochastic volatility --- p.27 / Chapter 5.3 --- The advantage of the Fourier transform method --- p.36 / Chapter 6. --- Conclusions --- p.41 / Chapter A. --- Measure change to risk neutral measure Q --- p.43 / Chapter B. --- Proof of integrability --- p.48 / Bibliography --- p.53