At first we introduce the Black-Scholes option pricing model, then by the assumption that the underlying asset pricing process is a general Ito stochastic process,i.

By analizing the behavior of underlying asset price and changing the basic assumption of Black Scholes option pricing model to the assumption that the underlying asset pricing process is a mixed process, we obtain the presentation of a new model for option pricing whose underlying asset pricing process is mixed process and improve some original results.

By analysing the behavior of underlying asset price, we obtain the presentation of a new model for option pricing based on mixed process, and attain the analytic formulas and the numerical methods of the new option pricing model.

In this paper, we mainly discuss the derivative security pricing problem for the untradable underlying assert.

The optimal hedge ratio of Shanghai and Shenzhen 300 stock index futures on the spot Shanghai and Shenzhen 300 index is calculated by establishing BGARCH model and analysis the effect of hedging in order to exam the effectiveness of setting Shanghai and Shenzhen 300 stock index as the underlying assets of the first stock index futures c.