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