A High Order Accurate Compact Finite Difference Method For Pricing American Option

In the past decades,establishing the option pricing theory is one of the most important developments in the financial field.Because option prices affect directly the earning and loss of buyers and sellers,it becomes a hot topic in the option pricing theory.American option is more complicated than European option and the study of American option pricing is the key question related to the option pricing theory.Recently,the regime-switching model has been widely used in many areas of finance,and many related good results have been obtained in the financial mathematics.Based on the previous research results,the objective of this thesis is to investigate the American option pricing based on the regime switching model by using a high-order accurate finite difference method.First,the stability and convergence on a fourth-order accurate,with respect to space,compact finite difference scheme for solving the Black-Scholes equation are analyzed by using the discrete energy method.The scheme is then tested by couple of examples.The obtained numerical results confirm the theoretical analysis.Second,American option prices with regime-switching,which satisfy a system of M free boundary value problems and thus make the problem much more difficult to solve,are considered.In this study,a fourth-order accurate compact finite difference scheme is developed by using an algebraic transformation to eliminate the first-order derivative with respect to space in the original system.Stability and convergence of the scheme are then analyzed using the discrete energy method.Numerical examples demonstrate the accuracy and applicability of the compact finite difference scheme.