基于最大熵和最小交叉熵方法的上证50ETF期权定价

Pricing Option of Shanghai 50ETF Based on the Methods of Maximum Entropy and Minimum Cross-Entropy

基于最大熵方法和最小交叉熵方法，给出了根据期权价格推断标的资产价格分布的模型和已知先验信息下推断标的资产价格分布的模型，利用拉格朗日乘子法给出了模型的简化解，通过粒子群算法求出标的资产价格的密度函数，进而对上证50ETF期权进行定价比较．实证结果表明：基于最大熵方法推断的分布可以作为标的资产价格分布的较好估计；基于最小交叉熵方法推断的分布是在先验信息下标的资产价格分布的较好估计，两种方法适用于我国上证50ETF期权定价．

The estimation of the distribution of an underlying asset from a set of option prices is developed with the principle of maximum entropy and minimum cross-entropy which allows the inclusion of prior knowledge of the asset distribution. The refined solution of model is obtained by using the Lagrange multiplier. This paper selects the Shanghai 50ETF option data and uses the particle swarm optimization algorithm to get the density function of the underlying asset which can be applied to pricing Shanghai 50ETF option. The results show that maximum entropy distribution can provide precise estimations of the underlying asset distribution and minimum cross entropy distribution performs well with prior knowledge. The methods can be applied to pricing options in China financial market.