The Research On Option Pricing Under Stochastic Volatility Market

Since options appear,option pricing has become a people's concerns.The famous option pricing formula Black-Scholes is an important turning point for pricing options,such pricing is not only displayed but also closer to the actual market at that time.But later it was found that such a pricing formula in the financial markets is limited,so this paper mainly do the following three aspects to improve and review the option pricing formula;First,in order to make the most classic option pricing formula closer to the real market value,combined with added volatility item before learning to make approximate solution closer to the real solution of this kind of thinking,using the perturbation method,the option for the solution of the classical equations obtained BS frist-order correction,and numerical examples prove that such a solution is closer to the actual value than classical solution;Second,select 3/2N stochastic volatility model,at the same time analysis and proof the existence of the analytic solution;Third,by changing standard Brownian motion in the classic formula of the option to the fractional Brownian motion,combined with exponential volatility model,derived the solution of the option driven by fractional Brownian motion with stochastic volatility.