The Differential Algorithms For Options Pricing Following Constant Elasticity Of Variance Model

"Financial Mathematic,Financial Project and Financial Management" constitute a significant research project specified by the National Foundation of Natural Science of China, in which option pricing theory is a problem of leading edge as well as a hot one.On the foundation of standard contract, more different characteristics exotic finance derivatives were designed in order to satisfy the finance market and the different investor especial needs, and keep away the risk which many investors might face, which including American option and binary option. Numerical solutions are displayed to advantage for such complex boundary issues.This thesis supposes that underlying asset value follows Constant Elasticity of Variance (CEV) model, which is the general of Black-Scholes model, based on the research of option characters. For the American put option and binary option which do not have analytical solution, we propose algorithms based on explicit scheme and implicit difference scheme and then prove that it is consistence, stable and convergent. The result of numerical example shows that the methods are effective and practical.