Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 51). Also available in electronic version. Access restricted to campus users.

Thesis ( (M.Sc.)(Mathematics and Applied Mathematics)--University of Pretoria, 2009. / Summary in English. Includes bibliographical references.

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Thesis (Ph. D.)--Ohio State University, 1978. / Includes vita. Includes bibliographical references (leaves 165-172). Available online via OhioLINK's ETD Center.

In the first part, we propose a non-zero-sum stochastic game approach of pricing convertible bond under the framework that the capital structure of the firm involves tax rebate and endogenous default policy. Convertible bond is a hybrid security which embodies characteristics of both straight bond and equity. Beyond the bond provisions, it endows a conversion option for the bondholder to convert the bond for the equity of the issuing firm and a call option for the firm to buy the debt back. The conflict of interests between bondholder and shareholder affects the security prices significantly. In Chapter 2, we investigate how to use a non-zero-sum game framework to model their interaction and to evaluate the convertible bond accordingly. Mathematically, this problem can be reduced down to a system of variational inequalities. After we clarify the structure of the optimal exercise region of both parties, we manage to explicitly derive a unique Nash equilibrium to the constraint game and specify the associated optimal exercise strategies. Our model shows that tax benefit and credit risk can produce considerable impact on the optimal strategies of both parties. The firm may issue a call when the debt is out-of-the-money or in-the-money. This is consistent with the empirical findings of "late and early calls" (Ingersoll (1977), Mikkelson (1981), Cowan et al. (1993) and Ederington et al. (1997)) . In addition, the optimal call policy under our model offers an explanation to some stylized patterns related to the returns of the company value as well. / In the second part, we use Laplace transform to study the pricing problems of various path-dependent exotic options with the underlying asset following an exponentially distributed jump diffusion process. These exotic options include double-barrier option and some occupation-time-related derivatives such as step options, corridor options, and quantile options. The result about double barrier options is presented in Chapter 3, where we prove non-singularity of a related high-dimensional matrix, which guarantees the existence and uniqueness of the solution. Chapter 4 is our work on occupation-time-related options, which presents an extension of the Black-Scholes setting to Kou's double-exponential jump diffusion model. We derive the closed-form Laplace transform of the joint distribution of the occupation time and the terminal value of the double-exponential jump diffusion process, and apply the result to price various occupation-time-related derivatives. This is done by solving the associated two correlated ordinary integro-differential equations, thanks to the special property of the exponential. All the Laplace transform-based analytical solutions can be inverted easily via Euler Laplace inversion algorithm, and the numerical results illustrate that our pricing methods are accurate and efficient. / Key words. Convertible Bond; Non-zero-sum Differential Game; Tax Benefit; Credit Risk; Early/Late Calls; Positive/Negative Stock Return; Double-barrier Options; Step Options; Corridor Options; Quantile Options; Occupation-Time; Jump-Diffusion Process. / This dissertation contains two parts: a non-zero-sum game approach of convertible bond and exotic options pricing under exponential-type jump-diffusion model. / Wan, Xiangwei. / Adviser: Nan Chen. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 157-170). / 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 Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

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The purpose of this thesis was to define and analyze the convertible hedge. It was an attempt at gaining perspective from which to make investment decision. It was recognized that it is a problem to maintain purchasing power of savings on a long-term basis. Even though, there is no infallible formula for the preservation of capital, it was felt that the investor can develop a financial plan in a manner which will tend to minimize risk and at the same time, provide ample profit potential by using the convertible hedge.The broad range of trading possibilities offered to the hedge investor was demonstrated by describing hypothetical and actual hedging positions. Based on this analysis, it was concluded that the convertible hedge is a trading technique that permits the investor to minimize risks and, at the same time, allows profits from stock movements in either direction.

No description available.

Abstract As Convertible Bonds (CB) market increasingly prospers in recent years, not only has it become one of the most important financing tools for public firms, but also the popular investment target for investors. However, given the complexity of Convertible Bonds Issuance Terms, coexistence of new and old regulations, and difficulties in obtaining relevant information, investors know little about CB in terms of its investment restrictions as well as arbitrage opportunities and models. This study attempts to explore arbitrage strategies for CB¡¦s trading and investing, and to design a CB ¡§Information System¡¨ which severs as a CB database querying system, and helps enhance the efficiency of CB investment and arbitrage. In this study, three CB related information systems were developed after analyzing CB issuance information and market price: 1. ¡§Database Querying System,¡¨ which is used to search for arbitrage restrictions and related information before engaging in CB investment and arbitrage. 2. ¡§Put Provision Instant Quoting System,¡¨ which is able to receive market quotation before exchange deadline, and to instantly calculate the rate of return in put provision. 3. ¡§Arbitrage Instant Quoting System,¡¨ like ¡§Put Provision Instant Quoting System,¡¨ can promptly calculate the rate of return in CB and considerably increase operating efficiency and the rate of return in arbitrage. Based on the case study and empirical research, this study argues that these three information systems can practically help control the fluctuation of market price, enhance operating efficiency, and serve as an effective financial operating tool of CB arbitrage strategies. Accordingly, several conclusions of this study are presented as follows: 1. The current stock market is inefficient, so the arbitrage opportunities are still available. 2. When market is thriving and stock price exceeds CB price, there are more arbitrage opportunities for and higher rate of return in CB. 3. While investing put provision for CB often accompanies high return opportunities, investors are suggested to gingerly evaluate the finance risks of public firms beforehand, such as making use of ¡§Instant Quoting System¡¨ to operate, which is helpful to controlling market price effectively. 4. To avoid operating risks, Investors should recognize all kinds of issuance restrictions in advance. 5. Conducting ¡§Instant Quoting System¡¨ can obtain market information quickly and promote operation efficiency and the rate of return.

No description available.