Numerical methods for option pricing under jump-diffusion models.

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.7Chapter 2 --- Parallel Talbot method for solving partial integro- differential equations --- p.9Chapter 2.1 --- Introduction --- p.9Chapter 2.2 --- Initial-boundary value problem --- p.11Chapter 2.3 --- Spatial discretization and semidiscrete problem --- p.12Chapter 2.4 --- Parallel Talbot method --- p.15Chapter 2.4.1 --- Φ-functions and Talbot quadrature --- p.15Chapter 2.4.2 --- Control on nonnormality and feasibility con- straints --- p.18Chapter 2.4.3 --- Optimal parameterization of parabolic Talbot contour --- p.22Chapter 2.5 --- Numerical experiments --- p.26Chapter 2.6 --- Conclusion --- p.32Chapter 3 --- Memory-reduction Monte Carlo method for pricing American options --- p.37Chapter 3.1 --- Introduction --- p.37Chapter 3.2 --- Exponential Levy processes and the full-storage method --- p.39Chapter 3.3 --- Random number generators --- p.41Chapter 3.4 --- The memory-reduction method --- p.43Chapter 3.5 --- Numerical examples --- p.45Chapter 3.5.1 --- Black-Scholes model --- p.46Chapter 3.5.2 --- Merton's jump-diffusion model --- p.48Chapter 3.5.3 --- Variance gamma model --- p.50Chapter 3.5.4 --- Remarks on the efficiency of the memory-reduction method --- p.52Chapter 3.6 --- Conclusion --- p.53Chapter 3.7 --- Appendix --- p.5