European Option Pricing With Uncertain Information Based On Generalized Rntropy Method

China's domestic SSE 50 ETF options started trading on the Shanghai Stock Exchange in 2015.In recent years,the trading volume of China's 50 ETF options has increased.Monthly trading volume reached 28.43 million in January 2018.Option is an important financial derivative product and the calculation of the premium is the core of the whole option theory.This paper's main contents are as follows:(1)In our paper,50ETF option is used as an example and it is found that the underlying asset 50ETF does not satisfy the lognormal distribution.Therefore,the generalized entropy method is used to price the 50ETF option.(2)Under the deterministic case,the maximum entropy model containing the constraint condition of the option price and the minimum cross entropy model with the constraint condition of the option price under the case of the known partial information are built.The Lagrangian multiplier method is used to solve the above two kinds of models.The models are applied to the 50ETF option and the characteristics of the asset price distribution at different times are studied.The distribution information of the underlying asset price can be used to price option and risk management.(3)In the case of uncertainty,the interval maximum entropy model with the constraint condition containing the interval option price is constructed.By using the interval number planning idea and setting the value of constraint satisfactory degree,the interval number programming problem is transformed into the deterministic programming problem.And the Lagrangian multiplier method is used to solve the deterministic programming model and the model is applied to the 50ETF option.The effect of the constraint satisfactory degree on the model is considered.The pricing and risk management of the option are carried out using the price distribution of the underlying asset.By comparing the pricing of the 50ETF option,it can be found that the generalized entropy method is suitable for the pricing of our options products.The research results of this paper put forward a new idea for option pricing.The generalized entropy method is a method to derive the true distribution of asset price according to the actual data of option price.This methods overcome the defects of many derivatives pricing models which assume the distribution of the underlying asset and can be used to price option and risk management.