Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: James S. Dyer. Vita. Includes bibliographical references.

Thesis (Ph. D. in Management)--Vanderbilt University, Aug. 2006. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Ehud Ronn. Vita. Includes bibliographical references and index.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 84-90). Also available in electronic version.

M.Comm. / Chapter 2 discussed the basic principles underlying of the two major option pricing formulae. It clearly showed that two totally different approaches were followed in each case, and yet both arrived at approximately the same value for the price of an option. Both these approaches made certain assumptions in their derivation of the formulae in order to simplify the final expressions, and to produce a more workable solution. They both however made substantial use of statistical probability in order to determine the likelihood of a certain event occurring. Chapter 3 gave a detailed derivation of both the Black and Scholes and the Binomial tree pricing formulae, as well as the associated criticism and advantages of the respective approaches. Value at risk, or VaR, was used in determining the statistical probability of a certain portfolio consisting of a specified option losing more than a certain percentage of its value over a given period of time. The resulting number obtained can be used to judge the riskiness of a portfolio in the given market conditions. All of these formulae are used on a daily basis by financial professionals in the daily operations of a magnitude of different institutions in order to value financial portfolios, the risk associated with these portfolios and the probability of certain events occurring within the portfolios in order to make better decisions and increase the profitability of these institutions, without actually knowing the underlying principles. - As- such these --formulae merely become a number crunching business, and interpretation of these numbers, without realising the pitfalls associated with the approaches in establishing these formulae. The random walk theory for unrestricted movement assumes that at t=0, the rates are at the origin. This can be interpreted as 0%, and instinctively any person would agree that 0% is not possible in any fixed income environment, due to the time value attached to money. Choosing the ruling rate as the origin would be more practical in determining the origin, but care must be taken in assigning probabilities to the up and down movements. At the onset of the problems amongst the emerging markets during 1998, the probability of rates increasing once it reached 17,00% was much higher than that of the rates decreasing. However, barely a month later when the rates had reached its peak at more than 21,00% and were declining again, the probability of the rates increasing once it reached 17,00% again was much lower than that of it decreasing further. This would have a significant effect on the probability generating function, and hence also an effect on the mean and variance thus derived. The probability curve of the rates during these times were also not represented by a standard normal curve, and as such the heteroscedacity of the curve had a major influence on the pricing of options. During extreme periods both the random walk theory and the Wiener process would be totally skewed, and unreliable answers would be derived from this approach. By 'adjusting the expression for a non-standard distribution, these problems can be eliminated and an accurate approach once again obtained using this process. Problems that could occur when using this approach to solve inaccuracies would amongst others include the following: The incorrect distribution function is being applied for the specific set of conditions prevailing in the market. This is due to the fact that under these abnormal conditions the distribution function can change over a very short period of time. Incorrect skews being applied to the distribution function due to fast changing market conditions. When to revert back to the normal distribution function. It then becomes a question not of an improper analytical approach, but incorrect timing approach. Since markets mostly perform according to the standardised normal distribution function the Wiener approach hold true for most applications.

University of Macau / Faculty of Science and Technology / Department of Mathematics

常方差彈性(CEV) 模型能夠刻畫波動率微笑的優點使之成為期權定價中的實用工具，然而它在應用到美式衍生工具時面臨分析上及計算上的挑戰。現行的解析方法是對代表著期權價格函數和其最佳履約曲線的自由邊界問題進行拉普拉斯卡森變換(LCT) ，繼而獲得在此變換下的解析解，可是此解含有合流超線幾何函數，使得它的數值計算在某些參數下顯得不穩定及低效。本文運用漸近法徹底解決美式期權在常方差彈性模型下的定價問題，並用永久性和限時性的美式看跌期權作為例子闡述所提出的方法。 / The constant elasticity of variance (CEV) model is a practical approach to option pricing by fitting to the implied volatility skew. Its application to American-style derivatives, however, poses analytical and numerical challenges. By taking the Laplace Carson transform (LCT) to the free-boundary value problem characterizing the option value function and the early exercise boundary, the analytical result involves confluent hyper-geometric functions. Thus, the numerical computation could be unstable and inefficient for certain set of parameter values. We solve this problem by an asymptotic approach to the American option pricing problem under the CEV model. We demonstrate the use of the proposed approach using perpetual and finite-time American puts. / Detailed summary in vernacular field only. / Pun, Chi Seng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 39-40). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Problem Formulation --- p.4 / Chapter 2.1 --- The CEV model --- p.4 / Chapter 2.2 --- The free-boundary value problem --- p.5 / Chapter 2.2.1 --- Perpetual American put --- p.5 / Chapter 2.2.2 --- Finite-time American put --- p.6 / Chapter 3 --- Asymptotic expansion of American put --- p.8 / Chapter 3.1 --- Perpetual American put --- p.8 / Chapter 3.2 --- Finite-time American put --- p.16 / Chapter 4 --- Numerical examples --- p.24 / Chapter 4.1 --- Perpetual American put --- p.24 / Chapter 4.2 --- Finite-time American put --- p.26 / Chapter 5 --- Conclusion --- p.29 / Chapter A --- Proof of Lemma 3.1 --- p.30 / Chapter B --- Property of ak --- p.32 / Chapter C --- Explicit formulas for u₂(S) --- p.34 / Chapter D --- Closed-form solutions --- p.37 / Bibliography --- p.40

Ng Chi-Tim. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 110-114). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.4 / Chapter Chapter 2 --- Mathematical Background --- p.7 / Chapter 2.1 --- Fractional Stochastic Integral --- p.8 / Chapter 2.2 --- Wick's Calculus --- p.9 / Chapter 2.3 --- Malliavin Calculus --- p.19 / Chapter 2.4 --- Fractional Ito's Lemma --- p.27 / Chapter Chapter 3 --- The Fractional Black Scholes Model --- p.34 / Chapter 3.1 --- Fractional Geometric Brownian Motion --- p.35 / Chapter 3.2 --- Arbitrage Opportunities --- p.38 / Chapter 3.3 --- Fractional Black Scholes Equation --- p.40 / Chapter Chapter 4 --- Generalization --- p.43 / Chapter 4.1 --- Stochastic Gradients of Fractional Diffusion Processes --- p.44 / Chapter 4.2 --- An Example : Fractional Black Scholes Mdel with Varying Trend and Volatility --- p.46 / Chapter 4.3 --- Generalization of Fractional Black Scholes PDE --- p.48 / Chapter 4.4 --- Option Pricing Problem for Fractional Black Scholes Model with Varying Trend and Volatility --- p.55 / Chapter Chapter 5 --- Alternative Fractional Models --- p.59 / Chapter 5.1 --- Fractional Constant Elasticity Volatility (CEV) Models --- p.60 / Chapter 5.2 --- Pricing an European Call Option --- p.61 / Chapter Chapter 6 --- Problems in Fractional Models --- p.66 / Chapter Chapter 7 --- Arbitrage Opportunities --- p.68 / Chapter 7.1 --- Two Equivalent Expressions for Geometric Brownian Motions --- p.69 / Chapter 7.2 --- Self-financing Strategies --- p.70 / Chapter Chapter 8 --- Conclusions --- p.72 / Chapter Appendix A --- Fractional Stochastic Integral for Deterministic Integrand --- p.75 / Chapter A.1 --- Mapping from Inner-Product Space to a Set of Random Variables --- p.76 / Chapter A.2 --- Fractional Calculus --- p.77 / Chapter A.3 --- Spaces for Deterministic Functions --- p.79 / Chapter Appendix B --- Three Approaches of Stochastic Integration --- p.82 / Chapter B.1 --- S-Transformation Approach --- p.84 / Chapter B.2 --- Relationship between Three Types of Stochastic Integral --- p.89 / Reference --- p.90

The development and introduction of financial derivatives have great impact on modern finance. Option pricing theory has become a powerful tool to value and to understand these innovations. It is also an indispensable tool to calculate hedge ratios for risk measurement and management. On the one hand, the introduction of new financial derivatives has been blamed for making financial market more volatile and risky as evidenced in the financial markets of the USA and Japan, especially during the expiration of index futures and index options, On the other hand, the applicability of new pricing models to hedging strategies is essential in monitoring and managing option positions. This study tries to give some answers on first: whether the expiration of financial derivatives increases the volatility of the Hong Kong stock market; second: whether we can better hedge by straightly applying more elaborated option valuation models replacing the standard Black-Scholes model, which market participants commonly employed for hedging option positions. Part I of this article addresses the first question while Part II studies the second question. / Yung Hei Ming. / Source: Dissertation Abstracts International, Volume: 62-09, Section: A, page: 3138. / Supervisor: Zhang Hua. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references. / 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. / Abstracts in English and Chinese. / School code: 1307.

published_or_final_version / Economics and Finance / Master / Master of Economics