An Exploration To Stability Of Volatility Function In AHBS Model

The classical Black-Scholes model(henceforth BS model) assumes that the price of the underlying stock follows geometric Brownian motion, at the same time, it assumes that the volatility is constant, which does not conform with the actual situation of the market. In fact, the implied volatility comes from the options market is not constant, it varies with the striking price and the time to maturity of the option, this phenomenon is what people observed-volatility smile. In order to overcome the lack of BS model and make sure that the model can more truly reflect the real market, many improved models are put forward by scholars on the basis of BS model, such as stochastic volatility model and deterministic implied volatility function model, etc. These models have an import effect on the research of option pricing theory.On the basis of previous studies, this paper structure multiple types of implied volatility function model by introducing different variables. Through the empirical analysis results we find that model3outperforms the other models. It is better to depict the BS implied volatility smile form. This analysis is based on two measures:root mean squared error(henceforth RMES), mean relative error(henceforth MRE). Either with RMSE or MRE, pricing errors produced by model3is minimum both in in-sample pricing performance and out-of-sample pricing performance. This paper has also established dynamic Black-Scholes implied volatility function model. Under the assumptions of a certain time to maturity, we discusses the effect of market information on the implied volatility function model, ulteriorly obtain the results of stable model structure.