published_or_final_version / Management Studies / Master / Master of Business Administration

published_or_final_version / Business Administration / Master / Master of Business Administration

published_or_final_version / Business Administration / Master / Master of Business Administration

published_or_final_version / abstract / Business / Master / Master of Philosophy

published_or_final_version / abstract / Real Estate and Construction / Doctoral / Doctor of Philosophy

published_or_final_version / Statistics / Master / Master of Philosophy

Exotic options are derivatives which have features that makes them more complex than vanilla traded products. Thus, finding their fair value is not always an easy task. We look at a particular example of the exotic options - the power option - whose payoffs are nonlinear functions of the underlying asset price. Previous analyses of the power option have only obtained solutions using probability methods for the case of the constant stock volatility and interest rate. Using Lie symmetry analysis we obtain an optimal system of the Lie point symmetries of the power option PDE and demonstrate an algorithmic method for finding solutions to the equation. In addition, we find a new analytical solution to the asymmetric type of the power option. We also focus on the more practical and realistic case of time dependent parameters: volatility and interest rate. Utilizing Lie symmetries, we are able to provide a new exact solution for the terminal pay off case. We also consider the power parameter of the option as a time dependent factor. A new solution is once again obtained for this scenario. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2013.

The purpose of this thesis is to compare the effectiveness of several interest rate models in fitting the true value of interest rates. Up until 1990, the universally accepted models were the equilibrium models, namely the Rendleman-Bartter model, the Vasicek model, and the Cox-Ingersoll-Ross (CIR) model. While these models were probably considered relatively accurate around the time of their discovery, they do not provide a good fit to the initial term structure of interest rates, making them substandard for use by traders in pricing interest rate options. The fourth model we consider is the Hull-White one-factor model, which does provide this fit. After calibrating, simulating, and comparing these four models, we find that the Hull-White model gives the best fit to our data sets. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

by Ng Shiu Cheong, Albert, Wong Shuk King, Grace. / Thesis (M.B.A.)--Chinese University of Hong Kong, 1991. / Bibliography: leaf 51. / ABSTRACT --- p.ii / TABLE OF CONTENT --- p.iv / ACKNOWLEDGEMENT --- p.vi / Chapter I. --- INTRODUCTION --- p.1 / General Background --- p.1 / Nature of rights issue --- p.2 / Reasons for company to raise funds through rights issue --- p.3 / Mechanics of rights offering --- p.3 / Underwriting rights issue --- p.4 / Trading of rights by shareholders --- p.4 / The intrinsic value of rights --- p.6 / Trading Rights in practice --- p.7 / Legal aspects of rights issue --- p.9 / Chapter II. --- VALUATION OF UNDERWRITING AGREEMENTS FOR RIGHTS ISSUES - THE BLACK AND SCHOLES MODEL --- p.11 / Introduction --- p.11 / Risks associated with rights issue --- p.12 / Underwriting agreement --- p.13 / The British versus American system --- p.14 / The Black and Scholes model --- p.16 / The Model --- p.16 / Empirical Findings of Underwriting Agreement --- p.18 / Comment --- p.19 / Chapter III. --- PRICING OF UNDERWRITING AGREEMENT IN HONG KONG --- p.20 / Basic Information --- p.20 / Option Pricing Model and Valuation of Underwriting Agreement --- p.21 / Assumed Price Model for Ex-post Stock Price in using Black-Scholes Model in Valuing Underwriting Agreement for Rights Issue --- p.22 / Methodology of study and Sampling --- p.23 / Estimation of variance of the stock's return --- p.25 / Hypothesis of Testing --- p.26 / Results of Analysis --- p.26 / Sensitivity of underwriting agreement value to the variables in the Black-Scholes model --- p.29 / Chapter IV. --- A NEW METHOD FOR PRICING THE UNDERWRITING AGREEMENTS FOR RIGHTS OFFERINGS --- p.35 / General overview --- p.36 / A New Price Model for the Ex-post Stock Price --- p.36 / The Model --- p.36 / Upper and Lower Bound for the Premium by K.K. Aase' s model --- p.38 / Analysis of Results --- p.40 / Chapter V. --- CONCLUSION --- p.43 / EXHIBIT 1 / "AMOUNT RAISED BY DIFFERENT METHODS IN THE MARKET, 1989" --- p.45 / APPENDIX 1 / LEGAL ASPECTS OF A RIGHTS ISSUES --- p.46 / BIBLIOGRAPHY --- p.51

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