The Further Discussion About American Options Pricing Under CEV Model

This paper is mainly in the study of American options previous various options under Constant Elasticity of Variance (CEV) model. The numerical algorithm model was probed further and the relationship between the elastic coefficient and option price was discussed principally.Firstly, this paper has established the model and made the simplification. The stability and convergence of research for this numerical algorithm of American options is conducted after simplification. The paper gets a stability condition of the algorithm, which is the theory evidence of elasticity coefficient valid interval .Secondly, this paper analyses the influence of elastic coefficient on the option price, and points out that under the CEV model, the influence factors of the price have two sides: fixed costs irrelevant to the stock price and the sensitivity of volatility to the stock change. As for put options, fixed costs hindering the rising prices will increase option value trend, however, this effect of the fixed assets of stock price in the influence of the reduction is reduced, leading the put option prices reduces; The option prices and volatility sensitivity was positively correlated. The two factors are reflected in elasticity coefficient and the two factors are interdependent; Introducing instance, mathematical software drew the chart expressing the relationship between CEV model's elastic coefficient and option price, and the problem that elasticity coefficient valid interval changes when the model step length changes is discussed .Finally, this paper points out that it can determine the two parameters in CEV model by fitting historical volatility. So we can get a method of determining the parameters, and use it for empirical research.