Research On Problems Of Stock Index Options Under Variety Models

Stock index option pricing mainly includes two aspects,one is to describe the movement of stock prices,the second is to choose the suitable equilibrium pricing method.In this paper,the classical Black-Scholes option pricing model is improved in order to accurately describe the movement of stock price.By using the stochastic differential and martingale and the actuarial approach method under the Vasicek interest rate model,the pricing formulas of options of improved model are obtained.The formulas not only generalize the classical Black-Scholes conclusion,but also contain the conclusions in the other literature.First of all the risk-free interest rate of the classical Black-Scholes option pricing model is improved by using the Vasicek interest rate model,the pricing formulas of European options are obtained.Second the distribution of Tsallis entropy,which has fat-tailed and long-term dependent characteristics,and O-U process,which describe the average resilience,and general Poisson jump-diffusion process,which describe the impact of non system factors,were selected to describe the law of the asset prices movement and the pricing formulas of options of improved model are obtained.The last we infer the options pricing estimating equation based on GARCH model which improved the constant volatility of the classical Black-Scholes option pricing model,and the pricing formulas of options of improved model are obtained.