The Pricing And Numerical Methods For Options With Stochastically Varying Volatility Of Underlying Assets Price

"Financial Mathematics,Financial Project and Financial Management" con-stitute 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 .This thesis gives a new evaluation method on the important factor—volatility, which has an important influence on the pricing of option, based on the research of option characters. It's shown in numerical examples results that, pricing on option by means of option pricing model with the aid of evaluation results become more accurate. For the American put option which does not have analytical solution,several new numerical algorithms are presented on its pricing, each of them is given finite difference method and finite element method on variables based on individual underlying variable and two underlying variable respectively. For finite element method, bilinear interpolation of rectangular sectioning is adopted. The result of numerical examples shows that the methods are effective and practical.