Analysis Of Option Pricing Under CEV Model

Option pricing problem has always been the hot topic of the financial industry. In this paper, firstly we analyses the classical CEV, through using the Kolmogorov forward equation and Feller lemma, we obtain the option pricing formula under this classical model, then we discuss the option pricing problem under this model with several different parameters, and get the corresponding option pricing formula. In which also includes the derivation of the classic Black-Scholes model. In the subsequent chapter, we deformed CEV model on the basis of the original CEV model. By considering the Kolmogorov backward equation of the deformed stochastic differential equation, we use the finite difference method, and finally get the numerical solution of the option under the deformed CEV model. At the end of this article, we takes some experiments under this model, especially about the pricing of American put option, and get good results.