by Lam Wing Shan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaf 41). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background on Option Pricing --- p.3 / Chapter 2.1 --- Financial options --- p.3 / Chapter 2.1.1 --- Basic terms of options --- p.3 / Chapter 2.1.2 --- Trading strategies --- p.4 / Chapter 2.1.3 --- The Principle of no Arbitrage --- p.5 / Chapter 2.1.4 --- Rational boundaries on Option Prices --- p.5 / Chapter 2.1.5 --- American Options --- p.6 / Chapter 2.1.6 --- Put-Call Parity --- p.7 / Chapter 2.2 --- Black-Scholes equation --- p.8 / Chapter 2.2.1 --- Derivation of Black-Scholes equation --- p.8 / Chapter 2.2.2 --- Solution to the Black-Scholes equation --- p.10 / Chapter 3 --- Review on Monte Carlo Method --- p.15 / Chapter 3.1 --- Monte Carlo Simulation --- p.15 / Chapter 3.2 --- Pricing an option using Monte Carlo Method --- p.18 / Chapter 3.3 --- Antithetic Variates Method --- p.21 / Chapter 4 --- Cell Partition Method --- p.23 / Chapter 4.1 --- An Advantage of the Cell Partition Method --- p.23 / Chapter 4.2 --- The Algorithm --- p.24 / Chapter 5 --- Numerical Results --- p.35 / Chapter 6 --- Conclusion --- p.39 / Bibliography --- p.41

Chan Chi-fai Quincy. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 52-55). / Abstracts in English and Chinese. / ACKNOWLEDGMENTS --- p.iv / LIST OF TABLES --- p.v / LIST OF ILLUSTRATIONS --- p.vi / CHAPTER / Chapter ONE --- INTRODUCTION --- p.1 / Chapter TWO --- LITERATURE REVIEW --- p.4 / Chapter THREE --- DATA AND METHODOLOGY --- p.8 / Moving Averages (MA) / Relative Strength Index (RSI) / Buy-and-Hold (B & H) and the Annual Return / Transaction Costs and the Adjusted Return / Chapter FOUR --- EMPIRICAL RESULTS --- p.13 / Hong Kong-HSI / Results Without Short Selling / Results With Short Selling / Results / Singapore - STII / Results Without Short Selling / Results With Short Selling / Results / Taiwan-TWSE / Results Without Short Selling / Results With Short Selling / Results / Korea-KSP / Results Without Short Selling / Results With Short Selling / Results / Chapter FIVE --- CONCLUSION --- p.30 / TABLES --- p.32 / ILLUSTRATIONS --- p.45 / BIBOGRAPHY --- p.52

Ren, You. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 48-51). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background of Option Pricing Theory --- p.1 / Chapter 1.2 --- American Option Pricing --- p.3 / Chapter 1.3 --- Numerical Approximation of American Option Price --- p.8 / Chapter 1.4 --- Statistical Issues --- p.12 / Chapter 1.4.1 --- Empirical Calibration --- p.13 / Chapter 2 --- Mixed Effects Model for American Option Prices --- p.16 / Chapter 2.1 --- Model --- p.16 / Chapter 2.2 --- Model Selection --- p.19 / Chapter 2.3 --- Empirical Bayes Prediction --- p.21 / Chapter 3 --- Simulation and Empirical Data --- p.22 / Chapter 3.1 --- Simulation --- p.22 / Chapter 3.1.1 --- Simulation of Stock Price Path and a Set of Options --- p.22 / Chapter 3.1.2 --- Training Mixed Effects Model --- p.27 / Chapter 3.1.3 --- Performance Measure and Prediction Result --- p.30 / Chapter 3.2 --- An Application to P&G American Options --- p.36 / Chapter 3.2.1 --- The Empirical Data and Setup --- p.36 / Chapter 3.2.2 --- Training Mixed Effects Option Pricing Model --- p.37 / Chapter 3.2.3 --- Performance Analysis --- p.41 / Chapter 4 --- Conclusion and Discussion --- p.46 / Bibliography --- p.48

Li, Xu. / Thesis submitted in: December 2008. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 41-43). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background Study --- p.6 / Chapter 3 --- Model Formulation --- p.8 / Chapter 3.1 --- Trading Cost Function --- p.9 / Chapter 3.2 --- Notations and Optimality Equation --- p.11 / Chapter 4 --- Optimal Policy --- p.14 / Chapter 4.1 --- Preliminary Assumption and Results --- p.14 / Chapter 4.1.1 --- "Generalized (s, 5, H) Policy" --- p.14 / Chapter 4.1.2 --- Polya Distribution and Quasi-K-convex --- p.15 / Chapter 4.1.3 --- Assumptions --- p.20 / Chapter 4.2 --- Single Period Problem --- p.23 / Chapter 4.3 --- Finite-Period Problem --- p.30 / Chapter 4.4 --- The Algorithm --- p.36 / Chapter 5 --- Conclusion --- p.39 / Bibliography --- p.41

Chan, Tsz Him. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 94-96). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Monte Carlo method in Finance --- p.6 / Chapter 2.1 --- Principle of MC and pricing theory --- p.6 / Chapter 2.2 --- An illustrative example --- p.9 / Chapter 3 --- Discretization method --- p.15 / Chapter 3.1 --- The Euler scheme and Milstein scheme --- p.16 / Chapter 3.2 --- Convergence of Mean Square Error --- p.19 / Chapter 4 --- Quasi Monte Carlo method --- p.22 / Chapter 4.1 --- Basic idea of QMC --- p.23 / Chapter 4.2 --- Application of QMC in Finance --- p.29 / Chapter 4.3 --- Another illustrative example --- p.34 / Chapter 5 --- Our Methodology --- p.42 / Chapter 5.1 --- Measure decomposition --- p.43 / Chapter 5.2 --- QMC in SDE simulation --- p.51 / Chapter 5.3 --- Towards a workable algorithm --- p.58 / Chapter 6 --- Numerical Result --- p.69 / Chapter 6.1 --- Case I Generalized Wiener Process --- p.69 / Chapter 6.2 --- Case II Geometric Brownian Motion --- p.76 / Chapter 6.3 --- Case III Ornstein-Uhlenbeck Process --- p.83 / Chapter 7 --- Conclusion --- p.91 / Bibliography --- p.96

Wu, Tao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 56-61). / Abstracts in English and Chinese. / Chapter 1 --- Background and Organization --- p.7 / Chapter 2 --- Parallel Talbot method for solving partial integro- differential equations --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.2 --- Initial-boundary value problem --- p.11 / Chapter 2.3 --- Spatial discretization and semidiscrete problem --- p.12 / Chapter 2.4 --- Parallel Talbot method --- p.15 / Chapter 2.4.1 --- Φ-functions and Talbot quadrature --- p.15 / Chapter 2.4.2 --- Control on nonnormality and feasibility con- straints --- p.18 / Chapter 2.4.3 --- Optimal parameterization of parabolic Talbot contour --- p.22 / Chapter 2.5 --- Numerical experiments --- p.26 / Chapter 2.6 --- Conclusion --- p.32 / Chapter 3 --- Memory-reduction Monte Carlo method for pricing American options --- p.37 / Chapter 3.1 --- Introduction --- p.37 / Chapter 3.2 --- Exponential Levy processes and the full-storage method --- p.39 / Chapter 3.3 --- Random number generators --- p.41 / Chapter 3.4 --- The memory-reduction method --- p.43 / Chapter 3.5 --- Numerical examples --- p.45 / Chapter 3.5.1 --- Black-Scholes model --- p.46 / Chapter 3.5.2 --- Merton's jump-diffusion model --- p.48 / Chapter 3.5.3 --- Variance gamma model --- p.50 / Chapter 3.5.4 --- Remarks on the efficiency of the memory-reduction method --- p.52 / Chapter 3.6 --- Conclusion --- p.53 / Chapter 3.7 --- Appendix --- p.54

This thesis considers the effect of stochastic skew in the interest rate cap and currency option markets, where we observe obvious stochastic variation of skew of implied volatility curve over time. To develop option pricing models consistent with empirical evidence, we adopt the Wishart process to model both stochastic volatility and stochastic skew of the asset return and to price options in both markets. As an affine model, the model is analytically tractable. Some distributional properties of the models are studied. The key feature of our model is that, when compared with the multi-factor Heston model, which generates stochastic skew through its volatility processes, the Wishart process contains not only volatility processes, but also volatility-unrelated processes which provide extra freedom to model the variation of skew that is not captured by the volatility processes. Numerical experiments demonstrate that the Wishart model has greater flexibility to model stochastic skew than the multi-factor Heston model in both the interest rate cap market and currency option market. Finally, results of calibration to market data and model estimation demonstrate the superiority of the Wishart model to the multi-factor Heston model in the interest rate cap market. / Ng, Hon Yip. / Advisers: Kwai-Sun Leung; Duan Li. / Source: Dissertation Abstracts International, Volume: 73-09(E), Section: A. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 89-98). / 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. / Abstract also in Chinese.

The aim of this thesis is to study multi-asset barrier options, where the volatilities of the stocks are assumed to define a matrix-valued bounded stochastic process. The bounds on volatilities may represent, for instance, the extreme values of the volatilities of traded options. As the volatilities are not known exactly, the value of the option can not be determined. Nevertheless, it is possible to calculate extreme values. We show that these values correspond to the best and the worst case scenarios of the future volatilities for short positions and long positions in the portfolio of the options. Our main tool is the equivalence of the option pricing and a certain stochastic control problem and the resulting concept of superhedging. This concept has been well known for some time but never applied to barrier options. First, we prove the dynamic programming principle (DPP) for the control problem. Next, using rather standard arguments we derive the Hamilton-Jacobi-Bellman equation for the value function. We show that the value function is a unique viscosity solution of the Hamilton-Jacobi-Bellman equation. Then we define the super price and superhedging strategy for the barrier options and show equivalence with the control problem studied above. The superprice price can be found by solving the nonlinear Hamilton-Jacobi-Equation studied above. It is called sometimes the Black-Scholes-Barenblatt (BSB) equation. This is the Hamilton-Jacobi-Bellman equation of the exit control problem. The sup term in the BSB equation is determined dynamically: it is either the upper bound or the lower bound of the volatility matrix, according to the convexity or concavity of the value function with respect to the stock prices. By utilizing a probabilistic approach, we show that the value function of the exit control problem is continuous. Then, we also obtain bounds for the first derivative of the value function with respect to the space variable. This derivative has an important financial interpretation. Namely, it allows us to define the superhedging strategy. We include an example: pricing and hedging of a single-asset barrier option and its numerical solution using the finite difference method.

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

published_or_final_version / Business / Doctoral / Doctor of Philosophy